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

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

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Article ID: iaor20173592
Volume: 78
Issue: 8
Start Page Number: 1438
End Page Number: 1448
Publication Date: Aug 2017
Journal: Automation and Remote Control
Authors: ,
Keywords: markov processes, stochastic processes, programming: nonlinear
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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