The procedure of excluding of the nonlinear trend fir the models described by stochastic differential and difference equations

TL;DR

This paper introduces a procedure to remove nonlinear trends from stochastic differential and difference equation models, enabling their analysis as simpler SDEs with reduced coefficients.

Contribution

It presents a novel method for excluding nonlinear growing trends in stochastic models with unbounded trends, applicable to both SDEs and Markov chains.

Findings

Procedure effectively reduces nonlinear trends in models.

Enables analysis of models with unbounded trends as simpler SDEs.

Applicable to both stochastic differential equations and Markov chains.

Abstract

We consider the diffusion process and its approximation by Markov chain with nonlinear increasing trends. The usual parametrix method is not appliable because these models have unbounded trends. We describe a procedure that allows to exclude nonlinear growing trend and move to stochastic differential equation with reduced drift and diffusion coefficients. A similar procedure is considered for a Markov chain