A note on exponential almost sure stability of stochastic differential equation

Xuerong Mao, Qingshuo Song, Dichuan Yang

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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.
Original languageEnglish
Pages (from-to)221-227
Number of pages7
JournalBulletin of the Korean Mathematical Society
Volume51
Issue number1
DOIs
Publication statusPublished - Jan 2014

Keywords

  • almost sure stability
  • Bessel squared process
  • Stochastic differential equations
  • regime-switching system
  • Lipschitz continuity

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