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

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Abstract

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.

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Authors and Affiliations

  1. National Research University Higher School of Economics, Moscow, Russia

    V. D. Konakov & A. R. Markova

Authors
  1. V. D. Konakov
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  2. A. R. Markova
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Correspondence to V. D. Konakov.

Additional information

Original Russian Text © V.D. Konakov, A.R. Markova, 2017, published in Avtomatika i Telemekhanika, 2017, No. 8, pp. 100–112.

This paper was recommended for publication by A.V. Nazin, a member of the Editorial Board

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Konakov, V.D., Markova, A.R. Nonlinear trend exclusion procedure for models defined by stochastic differential and difference equations. Autom Remote Control 78, 1438–1448 (2017). https://doi.org/10.1134/S0005117917080057

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  • DOI: https://doi.org/10.1134/S0005117917080057

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