A note on exponential almost sure stability of stochastic differential equation

Mao, Xuerong and Song, Qingshuo and Yang, Dichuan (2014) A note on exponential almost sure stability of stochastic differential equation. Bulletin of the Korean Mathematical Society, 51 (1). pp. 221-227. ISSN 2234-3016

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    Abstract

    Our goal is to relax a sufficient condition for the exponential almost sure stability of a certain class of stochastic differential equations. Compare to the existing theory, we prove the almost sure stability, replacing Lipschitz continuity and linear growth conditions by the existence of a strong solution of the underlying stochastic differential equation. This result is extendable for the regime-switching system. An explicit example is provided for the illustration purpose.