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A NOTE ON EXPONENTIAL ALMOST SURE STABILITY OF STOCHASTIC DIFFERENTIAL EQUATION

  • Mao, Xuerong (Department of Mathematics and Statistics University of Strathclyde) ;
  • Song, Qingshuo (Department of Mathematics and Statistics University of Strathclyde) ;
  • Yang, Dichuan (Department of Mathematics City University of Hong Kong)
  • Received : 2013.02.19
  • Published : 2014.01.31

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.

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