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Asymptotic Stability of Semi-Markov Modulated Jump Diffusions
Author
Source
International Journal of Stochastic Analysis
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-17, 17 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-08-23
Country of Publication
Egypt
No. of Pages
17
Main Subjects
Abstract EN
We consider the class of semi-Markov modulated jump diffusions (sMMJDs) whose operator turns out to be an integro-partial differential operator.
We find conditions under which the solutions of this class of switching jump-diffusion processes are almost surely exponentially stable and moment exponentially stable.
We also provide conditions that imply almost sure convergence of the trivial solution when the moment exponential stability of the trivial solution is guaranteed.
We further investigate and determine the conditions under which the trivial solution of the sMMJD-perturbed nonlinear system of differential equations dXt/dt=f(Xt) is almost surely exponentially stable.
It is observed that for a one-dimensional state space, a linear unstable system of differential equations when stabilized just by the addition of the jump part of an sMMJD process does not get destabilized by any addition of a Brownian motion.
However, in a state space of dimension at least two, we show that a corresponding nonlinear system of differential equations stabilized by jumps gets destabilized by addition of Brownian motion.
American Psychological Association (APA)
Deshpande, Amogh. 2012. Asymptotic Stability of Semi-Markov Modulated Jump Diffusions. International Journal of Stochastic Analysis،Vol. 2012, no. 2012, pp.1-17.
https://search.emarefa.net/detail/BIM-452783
Modern Language Association (MLA)
Deshpande, Amogh. Asymptotic Stability of Semi-Markov Modulated Jump Diffusions. International Journal of Stochastic Analysis No. 2012 (2012), pp.1-17.
https://search.emarefa.net/detail/BIM-452783
American Medical Association (AMA)
Deshpande, Amogh. Asymptotic Stability of Semi-Markov Modulated Jump Diffusions. International Journal of Stochastic Analysis. 2012. Vol. 2012, no. 2012, pp.1-17.
https://search.emarefa.net/detail/BIM-452783
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-452783