Asymptotic Stability in Probability Independent of Defining Stochastic Integrals

Abstract

This paper provides sufficient conditions for asymptotic stability in probability independend of defining stochastic integrals. We confirm that a stochatic integral over a Wiener process has an unknown parameter by revisiting Stratonovich's definition of stochastic integrals, derive an infinitesimal operator including the parameter, and then define a stability such that an equilibrium of a stochastic system keeps stability under any value of the parameter. A useful condition for a linear stochatic system is also derived.