On the exponential stability of switching-diffusion processes with jumps

Yuan, Chenggui; Bao, Jianhai

doi:10.1090/S0033-569X-2012-01292-8

Authors: Chenggui Yuan and Jianhai Bao
Journal: Quart. Appl. Math. 71 (2013), 311-329
MSC (2010): Primary 60H15; Secondary 60J28, 60J60
DOI: https://doi.org/10.1090/S0033-569X-2012-01292-8
Published electronically: October 18, 2012
MathSciNet review: 3087425
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Abstract: In this paper we focus on the pathwise stability of mild solutions for a class of stochastic partial differential equations which are driven by switching-diffusion processes with jumps. In comparison to the existing literature, we show that: (i) the criterion to guarantee pathwise stability does not rely on the moment stability of the system; (ii) the sample Lyapunov exponent obtained is generally smaller than that of the counterpart driven by a Wiener process; (iii) due to the Markovian switching the overall system can become pathwise exponentially stable although some subsystems are not stable.

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