Almost sure stability of some stochastic dynamical systems with memory

Alexandra Rodkina; Henri Schurz; Leonid Shaikhet

doi:10.3934/dcds.2008.21.571

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2008, Volume 21, Issue 2: 571-593. Doi: 10.3934/dcds.2008.21.571

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Almost sure stability of some stochastic dynamical systems with memory

1.
Department of Mathematics and Computer Science, The University of the West Indies, Mona, Kingston 7
2.
Southern Illinois University, Department of Mathematics, MC 4408, 1245 Lincoln Drive, Carbondale, IL 62901-7316
3.
Department of Higher Mathematics, Donetsk State University of Management, Chelyuskintsev str., 163-a, Donetsk, 83015

Received: April 2007

Revised: January 2008

Published: May 2008

Abstract / Introduction Related Papers Cited by

Abstract

Almost sure asymptotic stability of stochastic difference and differential equations with non-anticipating memory terms is studied in $\R^1$. Sufficient criteria are obtained with help of Lyapunov-Krasovskiĭ-type functionals, martingale decomposition and semi-martingale convergence theorems. The results allow numerical methods for stochastic differential equations with memory to be studied in terms of their ability to reproduce almost sure stability.

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Mathematics Subject Classification: Primary: 34F05, 60H10; Secondary: 37H10, 65C20.

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