On the exponential stability of switching-diffusion processes with jumps
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
Full-text PDF Free Access
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Additional Information
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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Additional Information
Chenggui Yuan
Affiliation:
Department of Mathematics, Swansea University, Swansea SA2 8PP, UK
Email:
C.Yuan@swansea.ac.uk
Jianhai Bao
Affiliation:
Department of Mathematics, Swansea University, Swansea SA2 8PP, UK
Email:
majb@swansea.ac.uk
Keywords:
Lévy noise,
maximal inequality,
exponential martingale inequality with jumps,
sample Lyapunov exponent
Received by editor(s):
July 6, 2011
Published electronically:
October 18, 2012
Article copyright:
© Copyright 2012
Brown University
The copyright for this article reverts to public domain 28 years after publication.