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A note on almost sure asymptotic stability of neutral stochastic delay differential equations with Markovian switching ☆

Li, Xiaoyue and Mao, Xuerong (2012) A note on almost sure asymptotic stability of neutral stochastic delay differential equations with Markovian switching ☆. Automatica, 48 (9). pp. 2329-2334. ISSN 0005-1098

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Abstract

In this paper, we consider neutralstochasticdelay differential equations with Markovian switching. Our key aim is to establish LaSalle-type stability theorems for the underlying equations. The key techniques used in this paper are the method of Lyapunov functions and the convergence theorem of nonnegative semi-martingales. The key advantage of our new results lies in the fact that our results can be applied to more general non-autonomous equations.