Terms Of Stochastic Differential Equations Research Articles

Stochastic modeling of carcinogenesis by state space models: a new approach

In this paper, we have developed some state space models for carcinogenesis involving multievent models and multiple pathways models. In these state space models, the stochastic system models are stochastic models of carcinogenesis expressed in terms of stochastic differential equations, whereas the observation models are statistical models based on the observed number of detectable preneoplastic lesions per individual over time and the observed number of detectable cancer tumors per individual over time. In this paper, we have applied some of the theories to some animal papillomas data from some initiation-promotion experiments on skin cancer in mice to estimate some unknown parameters. For this data set we have obtained excellent fit by a model with three piece-wise intervals.

Some exactly solvable models for the statistical evolution of internal variables during plastic deformation

A class of exactly solvable statistical models for the evolution of internal (microstructural) variables in the course of plastic deformation is discussed. The common feature of these models is that the microstructural evolution is described in terms of stochastic differential equations (Langevin equations) which by a non-linear transformation can be mapped onto a Wiener or Ornstein–Uhlenbeck process. Examples include the textural evolution of planar polycrystals, the evolution of dislocation density distribution in unidirectional plastic deformation, and the combined dynamics of mobile dislocations and dislocation obstacles leading to slip-channel formation.

Estimating the parameters of stochastic differential equations using a criterion function

Estimation of parameters in the drift and diffusion terms of stochastic differential equations involves simulation and generally requires substantial data sets. We examine a method that can be applied when available time series are limited to less than 20 observations per realisation. We compare and contrast parameter estimation for linear and nonlinear first-order stochastic differential equations using two criterion functions: one based on a Chi-square statistic. put forward by Hurn and Lindsay (1997), and one based on the Kolmogorov-Smirnov statistic. The estimates generated reflect the true parameter values well for all models. examined, especially when using the Kolmogorov-smirnov criterion function.

Stochastic Differential Equations of Pure-jumps in Relativistic Quantum Theory

The movement of relativistic quantum particles is described with pure-jump Markov processes in Nagasawas stochastic theory. Markov processes of pure-jumps are characterized in terms of stochastic differential equations of pure-jumps. The existence and uniqueness of solutions of stochastic differential equations of pure-jumps are shown under some regularity conditions. Markov processes of pure-jumps are then constructed with the help of the Schrödinger representation (process) . © 1999 Elsevier Science Ltd. All rights reserved.

Quantum stochastic differential equations in terms of quantum white noise

Quantum stochastic differential equations in terms of quantum white noise

A system of quantum stochastic differential equations in terms of non-equilibrium thermo field dynamics

Within the framework of non-equilibrium thermo field dynamics (NETFD), quantum Wiener processes at finite temperatures are constructed, and its representation space is shown to be the thermal space. After the introduction of the stochastic Shrodinger equation, a unified system of quantum stochastic differential equations, including the quantum stochastic Liouville equation and the quantum Langevin equation, is established within the quantum stochastic calculus.

A Random Exploration Approach for Automatic Chamferless Insertion

The stochastic approach strategy to realize the robotized in sertion of low-clearance, chamferless parts is studied in both the analytical and experimental contexts. The analytical ap proach is discussed in terms of stochastic differential equations that involve Gaussian white and colored noises processes to model a planar random search. Special attention is devoted to characterize the time required for the insertion, a random variable whose first moment calculation (i.e., the mean) is dealt with. In the mathematical modelization context adopted, it is remarkable that the calculated mean mating time grows slowly (i.e., logarithmically), with the precision required to perform an insertion. The. theoretical results are validated on a robo tized assembly system, also presented in this article. In this experimental system, the random movements are generated by pseudorandom binary sequences that, for the time scales con sidered, are large band processes. The experimental data are observed to sustain the logarithmic behavior obtained analyt ically. Hence, in addition to its simplicity and flexibility, the random strategy approach appears to be very efficient when high mating precision is required.

An alternative time series model of consumption: some empirical evidence

This paper presents some empirical evidence for a time series model of aggregate consumer' expenditure which is formulated in continuous time. It is argued that such models, expressed in terms of stochastic differential equations, are more realistic in representing the dynamic evolution of many economic time series, particularly at the aggregate level. However, such models impose complicated restrictions on the discretely observed data, which must be taken account of in estimation. The appropriate methodology is applied to a version of the consumption function for UK data, and is found to provide a good description of the data. The estimated continuous time model is compared with more popular discrete models, and is found to provide superior dynamic post-sample predictions over 16 quarters. The formulation of econometric models in continuous time may provide an alternative and potentially successful approach to the modelling of time series in many aspects of economics.

A hypothesis evaluation model for human operators

A study of a model that portrays the response of a person given a situation-assessment task is presented. The model is expressed in terms of stochastic differential equations in order that it be compatible with the usual modeling paradigm for describing dynamically varying situations. The measured response of a test subject has been compared with a sample response of a model. The subject was presented with a time-varying scene and was asked to indicate the level of confidence that a target was within the field of view. This, along with the actual locations of targets and decoys, was recorded and compared with the model response to the same scenario. The model did not reproduce the observed behavior pattern just as two humans would not respond identically to the same stimuli. Nevertheless, the model does manifest the 'human' indecisiveness found in the experiment.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Instantons in stochastic quantisation

Bosonic field theories may be formulated in terms of stochastic differential equations. The characteristic long term behaviour of these systems is a decay into the global minimum of their Hamiltonian. If local minima exist, the rate of this decay is determined by instanton effects. We calculate the decay rate and perform computer simulations on a 1 + 1 dimensional model to test the instanton approximation. We find the instanton approximations to be in very good agreement with the simulation results.

Comment on momentum in stochastic mechanics

Stochastic mechanics is a probabilistic description of quantum systems in terms of stochastic differential equations. Davidson [M. Davidson, Lett. Math. Phys. 5, 523 (1981)] and de Falco, De Martino, and De Siena [D. de Falco, S. De Martino, and S. De Siena, Lett. Nuovo Cimento 36, 457 (1983)] have introduced momentum variables into this scheme. In this paper a discussion of this attempt is presented and some difficulties concerning the physical interpretation are pointed out.

Measurement in stochastic mechanics

Stochastic mechanics is an explanation of nonrelativistic quantum phenomena in terms of stochastic differential equations. In this note a simple example of a measurement is constructed and the behavior of the sample paths of the corresponding stochastic differential equation is examined. The sample demonstrates that stochastic mechanics provides a natural explanation of the ’’reduction of the wave packet.’’

The relevance of stochastic calculus to cross correlation identification methods

The classical method of estimating the impulse response of a system by cross-correlating white noise input with output is formulated in terms of stochastic differential equations. This formulation is shown to indicate that different estimates of the impulse response near the origin can be obtained depending on the interpretation of the stochastic integral involved. An interpretation is given which leads to the correct estimate. These properties are demonstrated in a numerical example, and a numerical procedure that gives the correct estimate is pointed out.

A valid mathematical model for approximate nonlinear minimal-variance filtering

The problem considered herein is the continuous estimation of the state of a physical system undergoing random motion, where the knowledge of the motion is given by a known function of the state plus noise. The physical problem is abstracted to the extent that the random motion is considered to be a Markov process, and the noise is assumed to be white noise; consequently, the resulting mathematical problem is formulated in terms of stochastic differential equations. The optimal estimate for a minimal-variance criterion is known to be the conditional expectation of the state of the system given the measurements; the filter derived herein is a stochastic differential equation for an approximation to the optimal estimate. A formal derivation of a stochastic differential equation for an approximate nonlinear filter was presented by Bass et al. [l], based on an approach suggested by Kushner [2] and developed partially by Bucy [3]. It was later shown by Schwartz and Bass [4] that inherent in the approach is the assumption that the conditional probability density function is nearly completely contained in a neighborhood of the conditional expectation, and a new approximation was derived that replaced that assumption with the assumption that the conditional density is nearly Gaussian. The same filter was independently derived by Fisher [5].