Stochastic Rules Research Articles

A new hypervolume approach for assessing environmental risks

Assessing risks of uncertain but potentially damaging events, such as environmental disturbances, disease outbreaks and pest invasions, is a key analytical step that informs subsequent decisions about how to respond to these events. We present a continuous risk measure that can be used to assess and prioritize environmental risks from uncertain data in a geographical domain. The metric is influenced by both the expected magnitude of risk and its uncertainty. We demonstrate the approach by assessing risks of human-mediated spread of Asian longhorned beetle (ALB, Anoplophora glabripennis) in Greater Toronto (Ontario, Canada). Information about the human-mediated spread of ALB through this urban environment to individual geographical locations is uncertain, so each location was characterized by a set of probabilistic rates of spread, derived in this case using a network model. We represented the sets of spread rates for the locations by their cumulative distribution functions (CDFs) and then, using the first-order stochastic dominance rule, found ordered non-dominant subsets of these CDFs, which we then used to define different classes of risk across the geographical domain, from high to low. Because each non-dominant subset was estimated with respect to all elements of the distribution, the uncertainty in the underlying data was factored into the delineation of the risk classes; essentially, fewer non-dominant subsets can be defined in portions of the full set where information is sparse. We then depicted each non-dominant subset as a point cloud, where points represented the CDF values of each subset element at specific sampling intervals. For each subset, we then defined a hypervolume bounded by the outermost convex frontier of that point cloud. This resulted in a collection of hypervolumes for every non-dominant subset that together serve as a continuous measure of risk, which may be more practically useful than averaging metrics or ordinal rank measures.Overall, the approach offers a rigorous depiction of risk in a geographical domain when the underlying estimates of risk for individual locations are represented by sets or distributions of uncertain estimates. Our hypervolume-based approach can be used to compare assessments made with different datasets and assumptions.

Nonlinear Dynamic Boltzmann Machines for Time-Series Prediction

The dynamic Boltzmann machine (DyBM) has been proposed as a stochastic generative model of multi-dimensional time series, with an exact, learning rule that maximizes the log-likelihood of a given time series. The DyBM, however, is defined only for binary valued data, without any nonlinear hidden units. Here, in our first contribution, we extend the DyBM to deal with real valued data. We present a formulation called Gaussian DyBM, that can be seen as an extension of a vector autoregressive (VAR) model. This uses, in addition to standard (explanatory) variables, components that captures long term dependencies in the time series. In our second contribution, we extend the Gaussian DyBM model with a recurrent neural network (RNN) that controls the bias input to the DyBM units. We derive a stochastic gradient update rule such that, the output weights from the RNN can also be trained online along with other DyBM parameters. Furthermore, this acts as nonlinear hidden layer extending the capacity of DyBM and allows it to model nonlinear components in a given time-series. Numerical experiments with synthetic datasets show that the RNN-Gaussian DyBM improves predictive accuracy upon standard VAR by up to 35%. On real multi-dimensional time-series prediction, consisting of high nonlinearity and non-stationarity, we demonstrate that this nonlinear DyBM model achieves significant improvement upon state of the art baseline methods like VAR and long short-term memory (LSTM) networks at a reduced computational cost.

Decentralized Electric Vehicle Charging Strategies for Reduced Load Variation and Guaranteed Charge Completion in Regional Distribution Grids

A novel, fully decentralized strategy to coordinate charge operation of electric vehicles is proposed in this paper. Based on stochastic switching control of on-board chargers, this strategy ensures high-efficiency charging, reduces load variations to the grid during charging periods, achieves charge completion with high probability, and accomplishes approximate “valley-filling”. Further improvements on the core strategy, including individualized power management, adaptive strategies, and battery support systems, are introduced to further reduce power fluctuation variances and to guarantee charge completion. Stochastic analysis is performed to establish the main properties of the strategies and to quantitatively show the performance improvements. Compared with the existing decentralized charging strategies, the strategies proposed in this paper can be implemented without any information exchange between grid operators and electric vehicles (EVs), resulting in a communications cost reduction. Additionally, it is shown that by using stochastic charging rules, a grid-supporting battery system with a very small energy capacity can achieve substantial reduction of EV load fluctuations with high confidence. An extensive set of simulations and case studies with real-world data are used to demonstrate the benefits of the proposed strategies.

Robust Student’s t-Based Stochastic Cubature Filter for Nonlinear Systems With Heavy-Tailed Process and Measurement Noises

In this paper, a new robust Student's t-based stochastic cubature filter (RSTSCF) is proposed for a nonlinear state-space model with heavy-tailed process and measurement noises. The heart of the RSTSCF is a stochastic Student's t-spherical radial cubature rule (SSTSRCR), which is derived based on the third-degree unbiased spherical rule and the proposed third-degree unbiased radial rule. The existing stochastic integration rule is a special case of the proposed SSTSRCR when the degrees of freedom parameter tends to infinity. The proposed filter is applied to a maneuvering bearings-only tracking example, in which an agile target is tracked and the bearing is observed in clutter. Simulation results show that the proposed RSTSCF can achieve higher estimation accuracy than the existing Gaussian approximate filter, Gaussian sum filter, Huber-based nonlinear Kalman filter, maximum correntropy criterion-based Kalman filter, and robust Student's t-based nonlinear filters, and is computationally much more efficient than the existing particle filter.

Weak Convergence Rate of a Time-Discrete Scheme for the Heston Stochastic Volatility Model

The Heston stochastic volatility model is one of the most fundamental models in mathematical finance. In the literature, numerous efficient simulation methods have been proposed. However, there is no analytical weak convergence rate that applies to the full parameter regime, which is a long-standing problem. In this paper, we derive the weak convergence rate of a time-discrete scheme for the Heston stochastic volatility model, which employs the stochastic trapezoidal rule to discretize the logarithmic asset process, provided that the variance process is simulated exactly. The test function we consider for the error criterion can be any polynomials of the logarithmic asset process. We show that the analytical weak convergence rate is 2 for all parameter regimes. The result is consistent with the standard rate of the stochastic trapezoidal rule, although the coefficient of the model does not satisfy the global Lipschitz condition. Furthermore, in the majority of the literature, the analysis is based on assumptions on coefficients of SDEs, whereas we impose no direct conditions on the coefficient. Instead, we transfer the error analysis to that of a trapezoidal rule on a deterministic integral, on which we make some mild assumptions. Finally, we extend the scheme and the analysis for more general SDEs.

Blind hyperspectral unmixing by non-parametric non-Gaussianity measure

For linear mixing model (LMM) of hyperspectral unmixing in hyperspectral images processing problem, the endmember fractional abundances satisfy the sum-to-one constraint, which makes the well-known independent component analysis (ICA) based blind source separation (BSS) algorithms not well suited to blind hyperspectral unmixing (bHU). In this paper, an efficient non-parametric bHU algorithm consulting dependent component analysis (DCA) is presented. Based on the cumulative density function (CDF) and order statistics instead of traditional probability distribution function (PDF), the novel objective function is derived by maximising the non-parametric non-Gaussianity between the estimated endmember abundance of the endmember signatures and their corresponding original abundances. With the stochastic gradient rule of constrained optimisation method, an efficient dependent sources separation algorithm for bHU is obtained to fulfil the endmember signatures extraction and abundances estimation tasks. Simulations based on the synthetic data are performed to evaluate the validity of the proposed non-parametric non-Gaussianity HU (non-pNG-bHU) algorithm.

Adaptive Search Algorithms for Discrete Stochastic Optimization: A Smooth Best-Response Approach

This paper considers simulation-based optimization of the performance of a regime-switching stochastic system over a finite set of feasible configurations. Inspired by the stochastic fictitious play learning rules in game theory, we propose an adaptive simulation-based search algorithm that uses a smooth best-response sampling strategy and tracks the set of global optima, yet distributes the search so that most of the effort is spent on simulating the system performance at the global optima. The algorithm converges weakly to the set of global optima even when the observation data is correlated (as long as a weak law of large numbers holds). Numerical examples show that the proposed scheme yields a faster convergence for finite sample lengths compared with several existing random search and pure exploration methods in the literature.

Exploring Dynamic Environments Using Stochastic Search Strategies

In this paper, we conduct a literature review of laws of motion based on stochastic search strategies which are mainly focused on exploring highly dynamic environments. In this regard, stochastic search strategies represent an interesting alternative to cope with uncertainty and reduced perceptual capabilities. This study aims to present an introductory overview of research in terms of directional rules and searching methods mainly based on bio-inspired approaches. This study critically examines the role of animal searching behavior applied to random walk models using stochastic rules and kinesis or taxis. The aim of this study is to examine existing techniques and to select relevant work on random walks and analyze their actual contributions. In this regard, we cover a wide range of displacement events with an orientation mechanism given by a reactive behavior or a source-seeking behavior. Finally, we conclude with a discussion concerning the usefulness of using optimal foraging strategies as a reliable methodology.

Transboundary water allocation under water scarce and uncertain conditions: a stochastic bankruptcy approach

Designing a feasible and stable water sharing mechanism for transboundary river basins is a big challenge. The stochastic and uncertain characteristics of water flow in these rivers is among the main reasons which make the formation of cooperative coalitions with feasible water allocations and self-enforceable allocation agreements difficult. When the water in these river basins is scarce the task becomes even more challenging. This article focuses on the application of stochastic game theoretic extension of the bankruptcy concept to transboundary water resource sharing under water scarce and uncertain conditions. Among the water allocation vectors obtained from stochastic bankruptcy rules only the ones from the stochastic constrained equal awards rule were self-enforcing under uncertainty. Furthermore, the authors also proposed an allocation rule that can be used under a stochastic setting. The proposed rule provides water allocations that are self-enforcing in the absence of uncertainty. Generally, the application of the stochastic bankruptcy approach could be a source of important strategic information which can serve for the sustainable sharing and management of these vital sources of fresh water, particularly during water scarcity.

Multiple cross-correlation noise induced transition in a stochastic bistable system

Based on the stochastic equivalent rules, the Fokker–Planck Equation for a general one-dimensional nonlinear system subjected to N-component noises and cross-correlation noises is derived, and the greatest advantage of the method lies in its simplicity. Applying this method, the effects of multiple sources of noise and the correlation forms of noises among them (i.e., two multiplicative noises, an additive noise and the correlation between the three noises) on the steady-state properties and the mean first passage time (MFPT) of a stochastic bistable system are discussed in details. The results show rich transition phenomena, such as the reentrance-like noise-induced phenomenon and the switch between the bimodal and the unimodal structure for different noise intensities. Moreover, the effects of the cross-correlation among the three noise sources on the MFPT are also discussed, and the noise-enhanced stability phenomenon and the resonant activation phenomenon are observed. The numerical results are in basic agreement with the theoretical predictions.

Hybrid Cooperative Vehicle Positioning Using Distributed Randomized Sigma Point Belief Propagation on Non-Gaussian Noise Distribution

This paper proposes a cooperative positioning (CP) algorithm based on distributed modified sigma point belief propagation. Range measurement collected from the raw global navigation satellite systems (GNSSs) and ultra wide-band (UWB) data can be used for vehicle localization in urban areas under non-light-of-sight (NLOS) conditions. In order to alleviate the drawbacks of previous methods in handling non-Gaussian noise in NLOS and particularly in GNSS challenging environments, a newly range measurement error model is developed. The designed range measurement error model is based on a well-tailored non-Gaussian distribution for representing noise error in NLOS conditions. The CP problem is transformed into Bayesian inference on factor graph, which relies on a novel version of sigma point belief propagation (SPBP). The proposed CP algorithm is referred to hybrid cooperative non-Gaussian randomized sigma-point belief propagation (HC-ngR-SPBP). By using a nonlinear approximation based on randomized sigma points and stochastic integration rule (SIR), the HC-ngR-SPBP can: 1) reduce the number of sigma point and 2) solve a low computational cost the nonlinear measurement function exhibited by UWB and GNSS devices. The mean and the covariance calculated by the SIR are used to generate the non-Gaussian ranging probability density functions via the asymmetric generalized Gaussian mixture model. Simulation results conducted using various iterations with with real-time position information and range errors of 2 and 4 m demonstrate that the proposed algorithm outperforms the standard SPBP and nonparametric belief propagation and is very well suited for vehicle localization.

On exact and approximate stochastic dominance strategies for portfolio selection

One recent and promising strategy for Enhanced Indexation is the selection of portfolios that stochastically dominate the benchmark. We propose here a new type of approximate stochastic dominance rule which implies other existing approximate stochastic dominance rules. We then use it to find the portfolio that approximately stochastically dominates a given benchmark with the best possible approximation. Our model is initially formulated as a Linear Program with exponentially many constraints, and then reformulated in a more compact manner so that it can be very efficiently solved in practice. This reformulation also reveals an interesting financial interpretation. We compare our approach with several exact and approximate stochastic dominance models for portfolio selection. An extensive empirical analysis on real and publicly available datasets shows very good out-of-sample performances of our model.

Equity bargaining with common value

We study a common-value bilateral bargaining model with equity offer. In particular, we consider a model in which players bargain over an equity share of a common-value stochastic pie (i.i.d. over time) and players receive private signals on the size of the pie each period. Efficient agreement is a stochastic rule: Delay is efficient if the expected size of today’s pie is small and the discount factor is high. Hence, information aggregation is crucial for efficiency. We derive the conditions under which an equilibrium that attains the efficient agreement exists. The key idea is that the proposer makes an offer in such a way that the responder will use her signal if the responder’s signal is crucial for an efficient agreement.

Stochastic partially optimized cyclic shift crossover for multi-objective genetic algorithms for the vehicle routing problem with time-windows

This paper presents a stochastic partially optimized cyclic shift crossover operator for the optimization of the multi-objective vehicle routing problem with time windows using genetic algorithms. The aim of the paper is to show how the combination of simple stochastic rules and sequential appendage policies addresses a common limitation of the traditional genetic algorithm when optimizing complex combinatorial problems. The limitation, in question, is the inability of the traditional genetic algorithm to perform local optimization. A series of tests based on the Solomon benchmark instances show the level of competitiveness of the newly introduced crossover operator.

Comparison of different coupling schemes between counterions and charged nanoparticles in multiparticle collision dynamics.

We applied the multiparticle collision dynamics (MPC) simulation technique to highly asymmetric electrolytes in solution, i.e., charged nanoparticles and their counterions in a solvent. These systems belong to a domain of solute size which ranges between the electrolyte and the colloidal domains, where most analytical theories are expected to fail, and efficient simulation techniques are still missing. MPC is a mesoscopic simulation method which mimics hydrodynamics properties of a fluid, includes thermal fluctuations, and can be coupled to a molecular dynamics of solutes. We took advantage of the size asymmetry between nanoparticles and counterions to treat the coupling between solutes and the solvent bath within the MPC method. Counterions were coupled to the solvent bath during the collision step and nanoparticles either through a direct interaction force or with stochastic rotation rules which mimic stick boundary conditions. Moreover, we adapted the simulation procedure to address the issue of the strong electrostatic interactions between solutes of opposite charges. We show that the short-ranged repulsion between counterions and nanoparticles can be modeled by stochastic reflection rules. This simulation scheme is very efficient from a computational point of view. We have also computed the transport coefficients for various densities. The diffusion of counterions was found in one case to increase slightly with the volume fraction of nanoparticles. The deviation of the electric conductivity from the ideal behavior (solutes at infinite dilution without any direct interactions) is found to be strong.

A decision-making framework for river water quality management under uncertainty: Application of social choice rules

An important issue in river water quality management is taking into account the role played by wastewater dischargers in the decision-making process and in the implementation of any proposed waste load allocation program in a given region. In this study, a new decision-making methodology, called ‘stochastic social choice rules’ (SSCR), was developed for modeling the bargaining process among different wastewater dischargers into shared environments. For this purpose, the costs associated with each treatment strategy were initially calculated as the sum of treatment cost and the fines incurred due to violation of water quality standards. The qualitative simulation model (QUAL2Kw) was then used to determine the penalty function. The uncertainty associated with the implementation of strategies under the economic costs (i.e., the sum of treatment and penalty costs) was dealt with by a Monte-Carlo selection method. This method was coupled with different social choice methods to identify the best solution for the waste load allocation problem. Finally, using the extended trading-ratio system (ETRS), the most preferred treatment strategy was exchanged among dischargers as the initial set of discharge permits aimed at reducing the costs and encouraging dischargers to participate in the river water quality protection scheme. The proposed model was finally applied to the Zarjoub River in Gilan Province, northern Iran, as a case study. Results showed the efficiency of the proposed model in developing waste load allocation strategies for rivers.

A note on optimal portfolios under regime–switching

This paper extends the stochastic dominance rules for normal mixture distributions derived by Levy and Kaplanski (2015). First, the portfolios under consideration are allowed to follow different regime-switching processes. Second, the results are extended from second- to fourth-order stochastic dominance, which is known to be closely related to kurtosis aversion in financial markets and allows to compare mixture distributions with the same overall variance. In particular, when a risk-free asset is available, checking for fourth-order stochastic dominance turns out to amount to a comparison of the regime-specific and overall Sharpe ratios of the portfolios under consideration.

Stochastic rules for predator and prey hunting and escape behavior in a lattice-based model

Understanding of ecosystem resilience and stability requires comprehending predator–prey dynamics because ecosystems consist of dynamically interacting subsystems that include predator–prey relationships. This relationship is closely related to the hunting–escaping strategies employed by the predator and prey. Therefore, understanding the effects of hunting and escaping strategies on ecosystems will lead to a better understanding of these systems. As an approach for describing the predator–prey interaction, lattice-based models have been adopted because this approach has strong advantages for simulating various dynamical processes of individual–individual interaction. In the models, each lattice cell is either considered as an attractive/repulsive cell, or an individual cell, or else it is empty. The attractive (or repulsive cell) can be interpreted as the prey (or predator) of the individual. These states allow us to incorporate the ecological processes of local antagonistic interactions, namely the spread of disturbances (by the predator) and regrowth or recovery (by the prey). These processes are directly related to the strategic behavior of individuals, such as hunting and escaping. In this study, we suggest a simple and effective mapping formula as a stochastic rule to describe the hunting and escaping behavior. This formula could be widely used not only in the behavior but also in competitive and cooperative relationships.

Multi-Level Monte Carlo Simulation for the Heston Stochastic Volatility Model

We combine the Multi-level Monte Carlo (MLMC) method with the numerical scheme for the Heston model that simulates the variance process exactly and applies the stochastic trapezoidal rule to approximate the time integrated variance process in the SDE of the logarithmic asset process. We deal with the simulations for path-independent options and for path-dependent options separately. In both situations, novel MLMC estimators are established and the analytical convergence rates for these estimators are derived for the full parameter regime.

Stochastic Dominance: An Overall Review and an Empirical Evaluation on the Equity Premium Puzzle

This paper presents all the Stochastic Dominance (SD) rules (including Markowitz and Prospect Stochastic Dominance Rule), situations relating to these rules such as arbitrage, and several classes of preferences consistent to the SD approach. It also contains various algorithms for testing SD relations and necessary and sufficient conditions that may improve the efficiency of each Stochastic Dominance (SD) rule. Finally, it is examined the existence of the well-known equity premium puzzle in several economic environments, under different economic conditions and varying time horizons. The analysis is developed in a Stochastic Dominance framework using original evidence from three markets: US, UK and Germany market. The results show that stocks stochastically dominate bonds at second order (and at any higher order) for any time horizon, under different economic situations and for all international markets (US, UK and Germany market). This implies that stocks outperform bonds in a great percentage and thus the equity premium puzzle is real and quite robust.