Xuerong Mao, Qingshuo Song, and Dichuan Yang University of Strathclyde, City University of Hong Kong, City University of Hong Kong
Abstract : Our goal is to relax a sufficient condition for the exponential almost sure stability of a certain class of stochastic differential equations. Compared 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.
Keywords : almost sure stability, stochastic differential equation, regime-switching, Besel squared process