Automation and Remote Control

, Volume 78, Issue 8, pp 1438–1448 | Cite as

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

  • V. D. KonakovEmail author
  • A. R. Markova
Stochastic Systems


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.


stochastic differential equation diffusion process Markov chains parametrix method 


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Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.National Research University Higher School of EconomicsMoscowRussia

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