Linearization and local stability of random dynamical systems

TL;DR

This paper investigates the local stability of random dynamical systems using linearization techniques, providing theoretical results applicable to general metric and Banach spaces, with applications demonstrated in mathematical finance.

Contribution

It introduces new stability criteria for random dynamical systems in metric and Banach spaces based on linearization, extending existing theory.

Findings

Stability conditions established for systems in metric spaces

Linearization approach effective in Banach space analysis

Applications demonstrated in mathematical finance

Abstract

The paper examines questions of local asymptotic stability of random dynamical systems. Results concerning stochastic dynamics in general metric spaces, as well as in Banach spaces, are obtained. The results pertaining to Banach spaces are based on the linearization of the systems under study. The general theory is motivated (and illustrated in this paper) by applications in mathematical finance.