Nonlinear trend exclusion procedure for models defined by stochastic differential and difference equations

We consider a diffusion process and its approximation with a Markov chain whose trends contain a nonlinear unbounded component. The usual parametrix method is inapplicable here since the trend is unbounded. We present a procedure that lets us exclude a nonlinear growing trend and pass to a stochasti...

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Bibliographic Details
Published inAutomation and remote control Vol. 78; no. 8; pp. 1438 - 1448
Main Authors Konakov, V. D., Markova, A. R.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.08.2017
Springer Nature B.V
Subjects
CAE) and Design
Calculus of Variations and Optimal Control; Optimization
Computer-Aided Engineering (CAD
Control
Difference equations
Differential equations
Markov analysis
Markov chains
Mathematics
Mathematics and Statistics
Mechanical Engineering
Mechatronics
Robotics
Stochastic Systems
Systems Theory
Trends
Markov chains
parametrix method
diffusion process
stochastic differential equation
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Summary:We consider a diffusion process and its approximation with a Markov chain whose trends contain a nonlinear unbounded component. The usual parametrix method is inapplicable here since the trend is unbounded. We present a procedure that lets us exclude a nonlinear growing trend and pass to a stochastic differential equation with bounded drift and diffusion coefficients. A similar procedure is also considered for a Markov chain.
ISSN:0005-1179
1608-3032
DOI:10.1134/S0005117917080057