This article is cited in 5 papers

Theorems of comparison and stability with probability 1 for one-dimensional stochastic differential equations

A. S. Asylgareev, F. S. Nasyrov

Ufa State Aviation Technical University, Ufa, Russia

Abstract: We prove the comparison theorems for scalar stochastic differential equations in the case of different diffusion coefficients. Conditions are given of stability with probability 1 with respect to the trivial solution to stochastic differential equations with random coefficients. The results remain valid for deterministic analogs of stochastic differential equations with symmetric integrals.

Keywords: equation with symmetric integrals, stochastic differential equation, stability with probability 1, comparison theorem.

UDC: 519.2

Received: 07.06.2015

DOI: 10.17377/smzh.2016.57.502

 English version: Siberian Mathematical Journal, 2016, 57:5, 754–761

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