Application of Approximation Methods of Iterated Stratonovich and Ito Stochastic Integrals to Numerical Simulation of Controlled Stochastic Systems

Dmitriy F. Kuznetsov

doi:10.1615/jautomatinfscien.v31.i10.100

Application of Approximation Methods of Iterated Stratonovich and Ito Stochastic Integrals to Numerical Simulation of Controlled Stochastic Systems

Journal of Automation and Information Sciences ◽

10.1615/jautomatinfscien.v31.i10.100 ◽

1999 ◽

Vol 31 (10) ◽

pp. 70-83

Author(s):

Dmitriy F. Kuznetsov

Keyword(s):

Numerical Simulation ◽

Stochastic Systems ◽

Stochastic Integrals ◽

Approximation Methods

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Numerical Simulation of Dynamic Stability of Fractional Stochastic Systems

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455418501286 ◽

2018 ◽

Vol 18 (10) ◽

pp. 1850128 ◽

Cited By ~ 2

Author(s):

Jian Deng

Keyword(s):

Numerical Simulation ◽

Lyapunov Exponent ◽

Dynamic Stability ◽

Stochastic Systems ◽

Simulation Method ◽

Largest Lyapunov Exponent ◽

Stochastic Dynamic ◽

Data Normalization ◽

Moment Lyapunov Exponent ◽

The Largest Lyapunov Exponent

The modern theory of stochastic dynamic stability is founded on two main exponents: the largest Lyapunov exponent and moment Lyapunov exponent. Since any fractional viscoelastic system is indeed a system with memory, data normalization during iterations will disregard past values of the response and therefore the use of data normalization seems not appropriate in numerical simulation of such systems. A new numerical simulation method is proposed for determining the [Formula: see text]th moment Lyapunov exponent, which governs the [Formula: see text]th moment stability of the fractional stochastic systems. The largest Lyapunov exponent can also be obtained from moment Lyapunov exponents. Examples of the two-dimensional fractional systems under wideband noise and bounded noise excitations are presented to illustrate the simulation method.

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Gillespie algorithm and diffusion approximation based on Monte Carlo simulation for innovation diffusion: A comparative study

Monte Carlo Methods and Applications ◽

10.1515/mcma-2019-2040 ◽

2019 ◽

Vol 25 (3) ◽

pp. 209-215

Author(s):

Nikhil Kumar Rajput

Keyword(s):

Monte Carlo Simulation ◽

Monte Carlo ◽

Comparative Study ◽

Innovation Diffusion ◽

Diffusion Approximation ◽

Information Diffusion ◽

Stochastic Systems ◽

Gillespie Algorithm ◽

Approximation Methods ◽

Sample Paths

Abstract Monte Carlo simulations have been utilized to make a comparative study between diffusion approximation (DA) and the Gillespie algorithm and its dependence on population in the information diffusion model. Diffusion approximation is one of the widely used approximation methods which have been applied in queuing systems, biological systems and other fields. The Gillespie algorithm, on the other hand, is used for simulating stochastic systems. In this article, the validity of diffusion approximation has been studied in relation to the Gillespie algorithm for varying population sizes. It is found that diffusion approximation results in large fluctuations which render forecasting unreliable particularly for a small population. The relative fluctuations in relation to diffusion approximation, as well as to the Gillespie algorithm have been analyzed. To carry out the study, a nonlinear stochastic model of innovation diffusion in a finite population has been considered. The nonlinearity of the problem necessitates use of approximation methods to understand the dynamics of the system. A stochastic differential equation (SDE) has been used to model the innovation diffusion process, and corresponding sample paths have been generated using Monte Carlo simulation methods.

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Volterra equations with fractional stochastic integrals

Mathematical Problems in Engineering ◽

10.1155/s1024123x04312020 ◽

2004 ◽

Vol 2004 (5) ◽

pp. 453-468 ◽

Cited By ~ 13

Author(s):

Mahmoud M. El-Borai ◽

Khairia El-Said El-Nadi ◽

Osama L. Mostafa ◽

Hamdy M. Ahmed

Keyword(s):

Integral Equations ◽

Stochastic Systems ◽

Volterra Equations ◽

Stochastic Integrals ◽

Fractional Systems ◽

Black Scholes ◽

Systems Of Integral Equations

Some fractional stochastic systems of integral equations are studied. The fractional stochastic Skorohod integrals are also studied. The existence and uniquness of the considered stochastic fractional systems are established. An application of the fractional Black-Scholes is considered.

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