Jump Process Research Articles

Seeing the root of the problem of student independence during the Covid-19 pandemic, implementing the effectiveness of learning with the Seven Jumps model assisted by the whatsapp group during the Covid-19 Pandemic is the aim of this research. This type of research approach is a qualitative and quantitative experiment carried out online with the Seven Jumps learning model assisted by WhatsApp groups. Data was collected by questionnaires, observation sheets and tests. Valid device tests come from expert perceptions, test the effectiveness of learning with statistical tests of the effect of regression and comparative t tests. The results showed that the root problems and constraints for student independence in utilizing information technology to achieve the expected competencies were: low self-motivation to learn, self-assessment ability, self-discipline, self-control, responsibility, pattern-learning ability, self-reliance in designing appropriate learning objectives, design implementation strategies, monitoring the progress of learning outcomes, coordination of learning methods, and the need for guidance in finding learning resources, implementing independent learning with the Seven Jumps model assisted by the whatsapp group is effective. This is indicated by: a) there is a positive influence of independent learning on problem solving ability of 60.8%, b) The gain test to measure the effectiveness of the pretest and posttest is 0.52 in the medium category and the effectiveness is sufficient. The Seven Jumps method can be implemented boldly during the Covid-19 Pandemic.

In this article, observed-based discrete proportion-integration-differentiation (PID) control for multi-area interconnected power systems is addressed under hybrid attacks. Firstly, a reconstructed jump model for interconnected power systems is proposed by taking the circumstance of data packet loss into consideration, which caused by the stochastic transmission delay of sampled data. Then, different from the traditional continuous-type PID control, an observer-based discrete-type PID control strategy is designed for discrete-time power system. Besides, due to the sampled data may be tampered or shield in open communication networks, the hybrid attacks, i.e., deception attacks and denial-of-service attacks, with random manners are considered. Furthermore, an input-to-state stable criterion is derived by constructing appropriate Lyapunov-Krasovskii functionals. Finally, the discrete-type PID controllers and observer are achieved, and the validity of proposed approach are also demonstrated in the illustrative examples section.

This study aimed to address the shortcomings of the Seven Jump learning model by developing and evaluating a new learning model called the Ten Jump model. The research was conducted in class C with 42 nursing students in the 2022/2023 academic year using the ADDIE method. The validity, practicality, and effectiveness of the Ten Jump model were evaluated based on validation results, lecturer and student activities, and student learning outcomes. The findings suggest that the Ten Jump model is a valid, practical, and effective learning model, with validation results over 90%, comprehensive application of learning model syntax, and N-Gain values over 70% representing improved student learning outcomes. The study also found positive student responses, indicating that the Ten Jump model can enhance soft skill learning.

The cryptocurrency market is volatile, non-stationary and non-continuous. Together with liquid derivatives markets, this poses a unique opportunity to study risk management, especially the hedging of options, in a turbulent market. We study the hedge behaviour and effectiveness for the class of affine jump diffusion models and infinite activity Lévy processes. First, market data is calibrated to stochastic volatility inspired-implied volatility surfaces to price options. To cover a wide range of market dynamics, we generate Monte Carlo price paths using an stochastic volatility with correlated jumps model, a close-to-actual-market GARCH-filtered kernel density estimation as well as a historical backtest. In all three settings, options are dynamically hedged with Delta, Delta–Gamma, Delta–Vega and Minimum Variance strategies. Including a wide range of market models allows to understand the trade-off in the hedge performance between complete, but overly parsimonious models, and more complex, but incomplete models. The calibration results reveal a strong indication for stochastic volatility, low jump frequency and evidence of infinite activity. Short-dated options are less sensitive to volatility or Gamma hedges. For longer-dated options, tail risk is consistently reduced by multiple-instrument hedges, in particular by employing complete market models with stochastic volatility.

Sliding mode control for discrete-time singular semi-Markovian jumping models

Most structural models for valuing corporate securities assume a geometric Brownian motion to describe the value of a firm’s assets. However, this does not reflect market stylized features: the default is more often driven by unexpected information and sudden shocks, which are not captured by the Gaussian model assumption. To remedy this, we propose a dynamic program for valuing corporate securities under various Lévy processes. Specifically, we study two jump diffusions and a pure-jump process. Under these settings, we build and experiment with a flexible framework that accommodates the balance-sheet equality, arbitrary corporate debts, multiple seniority classes, tax benefits and bankruptcy costs. While our approach applies to several Lévy processes, we compute and detail the total value of equity, the total value of debt and the total value of the firm as well as the credit spreads of the debt by using Gaussian, double exponential and variance-gamma jump models.

<abstract> <p>Exchange rate is an important part of financial markets. Our analysis finds that the fluctuations of exchange rates have several obvious features, such as spikes, thick tails, fluctuation aggregations and asymmetry. Based on this, we build novel GARCH class model by introducing a jumping process to describe the dynamics of their fluctuations. Our empirical results show that the models with jump factors can better characterize the agglomeration and thick tail characteristics of these return fluctuations than the models without jump factors. In particular, the model with double exponential jumps can fully handle and capture the fluctuation characteristics of the returns. Our findings will be useful for individuals and governments to predict exchange rate fluctuations, provide reference for the effective management of exchange rate risk in China, and further improve the financial risk management mechanism.</p> </abstract>

Variable Jump Models in High Frequency Market Processes

Continuous Statistical Jump Models for Identifying Financial Regimes

Studies have shown that stock price process exhibits long-range dependence. To address this, many have introduced the mixed-fractional Brownian motion (MFBM) model to the stock price process. Under risk-neutral measure, this study provides an analytical formula for the price of European-style power call options in an MFBM environment with the inclusion of the jumps process. Modeling the stock price with MFBM and jumps process enables the capturing of long memory trend as well as discontinuity in the stock price process.

Modeling oil–mist filtration through coalescence filter media in the presence of gravity-induced flows

The Fenna–Mathews–Olson(FMO) complex present ingreen sulfur bacteria is known to mediate the transfer of excitationenergy between light-harvesting chlorosomes and membrane-embeddedbacterial reaction centers. Due to the high efficiency of this transportprocess, it is an extensively studied pigment–protein complexsystem with the eventual aim of modeling and engineering similar dynamicsin other systems and using it for real-time application. Some studieshave attributed the enhancement of transport efficiency to wavelikebehavior and non-Markovian quantum jumps resulting in long-lived andrevival of quantum coherence, respectively. Since dynamics in thesesystems reside in the quantum-classical regime, quantum simulationof such dynamics will help in exploring the subtle role of quantumfeatures in enhancing the transport efficiency, which has remainedunsettled. Discrete simulation of the dynamics in the FMO complexcan help in efficient engineering of the heat bath and controllingthe environment with the system. In this work, using the discretequantum jump model we show and quantify the presence of higher non-Markovianmemory effects in specific site pairs when internal structures andenvironmental effects are in favor of faster transport. As a consequence,our study leans toward the connection between non-Markovianity inquantum jumps with the enhancement of transport efficiency.

How macrostructures enhance droplet coalescence jumping: A mechanism study

We investigate the local equilibrium (LE) distribution of a crystal surface jump process as it approaches its hydrodynamic (continuum) limit in a nonstandard scaling regime introduced by Marzuola and Weare. The atypical scaling leads to a local equilibrium state whose structure is novel to the best of our knowledge. The distinguishing characteristic of the new, rough LE state is that the ensemble average of single lattice site observables do not vary smoothly across lattice sites. We investigate numerically and analytically how the rough LE state affects the convergence mechanism via three key limits, and we show that by comparison more standard, “smooth” LE states satisfy stronger versions of these limits.

Droplets coalesce and jump from superhydrophobic surfaces, a result that stems from the dominance of capillary and inertial forces and the presence of high contact angles. This phenomenon has been a subject of intensive numerical research mostly for cases when the degree of hydrophobicity is described by a single contact-angle value (a static contact angle). The introduction of various degrees of contact-angle hysteresis complicates the numerical modeling of the jumping process due to the sensitivity of the results to the effective value of the contact angle. We have developed and validated a comprehensive volume-of-fluid–immersed boundary numerical framework that accounts for the effect of hysteresis by focusing on the representation of actual (i.e., effective) values of contact angles. By comparing the behavior of jumping droplets on superhydrophobic surfaces with several degrees of hysteresis (up to 15°), we quantified the influence of hysteresis on the jumping process and identified various stages of the merged droplet's detachment and re-attachment to the surface. The latter phenomena were observed in all our simulations with droplets of different initial radii. In all the cases with hysteresis, the merged droplet eventually jumps, but we point out the decrease in the jumping velocity as compared to cases with only a static contact angle imposed. Finally, by using the Kistler dynamic contact-angle model, we demonstrate and quantify the importance of accurately capturing the dynamic receding contact angle when droplets jump from superhydrophobic surfaces with various degrees of hysteresis.

Coalescence-induced jumping of in-plane moving droplets: Effects of initial velocity and sideslip angle

In addition to the characteristics of leptokurtic fat-tailed distribution, financial sequences also exhibit typical volatility and jumps. Moreover, jumps exhibit self-exciting and clustering characteristics under extreme events. However, studies on dynamic margin levels often ignore jumps. In this study, we combine the self-exciting stochastic volatility with correlated jumps (SE-SVCJ) model with a generalized Pareto distribution (GPD) to measure the optimal margin level for the stock index futures market. Value at risk (VaR) is estimated and forecasted using the SE-SVCJ-GPD, SVCJ-GPD, and generalized autoregressive conditional heteroskedasticity with GPD (GARCH-GPD) models. SE-SVCJ-GPD can undertake more risks in the long or short trading position of stock index futures contracts. Moreover, the backtesting experiment results show that the SE-SVCJ-GPD model provides a more accurate margin level forecast than the other methods in both positions. This study’s findings have practical significance and theoretical value for assessing the level of risk and taking corresponding risk-prevention measures.

Coalescence-induced droplet jumping could promote self-removal of droplets, which has broad potential in related fields such as heat-transfer enhancement, self-cleaning, energy harvesting, electricity generation, radiative cooling, and antifrosting/icing. In practical applications, droplets often have initial velocity under external forces. In this work, the coalescence-induced jumping of centripetal moving droplets on a superhydrophobic plane is experimentally observed using a high-speed photography platform, and the effects of the initial velocity of the moving droplet on jumping velocity, energy conversion, and droplet morphology are numerically investigated. Results show that the jumping velocity decreases and then increases as the We number of the moving droplet increases. The main source of the total kinetic energy of the coalesced droplet switches from the released surface energy to the initial kinetic energy of the moving droplet with the increasing We number, but the proportion of the jumping kinetic energy to the total kinetic energy decreases. Besides, the initial velocity of the moving droplet intensifies the droplet deformation and accelerates the process of coalescence-induced jumping. Through theoretical analysis, it is found that the jumping velocity is affected by two mechanisms: the deformation intensification and the liquid bridge impact enhancement.

We derive a universal, exact asymptotic form of the splitting probability for symmetric continuous jump processes, which quantifies the probability π_{0,[under x]_}(x_{0}) that the process crosses x before 0 starting from a given position x_{0}∈[0,x] in the regime x_{0}≪x. This analysis provides in particular a fully explicit determination of the transmission probability (x_{0}=0), in striking contrast with the trivial prediction π_{0,[under x]_}(0)=0 obtained by taking the continuous limit of the process, which reveals the importance of the microscopic properties of the dynamics. These results are illustrated with paradigmatic models of jump processes with applications to light scattering in heterogeneous media in realistic 3D slab geometries. In this context, our explicit predictions of the transmission probability, which can be directly measured experimentally, provide a quantitative characterization of the effective random process describing light scattering in the medium.

Volatility analysis for the GARCH–Itô–Jumps model based on high-frequency and low-frequency financial data