A note on exponential almost sure stability of stochastic differential equation
Bull. Korean Math. Soc. 2014 Vol. 51, No. 1, 221-227
https://doi.org/10.4134/BKMS.2014.51.1.221
Printed January 1, 2014
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
MSC numbers : 60G52, 60G17
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