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This paper aims to study stability in distribution of Markovian switching jump diffusions. The main motivation stems from stability and stabilizing hybrid systems in which there is no trivial solution. An explicit criterion for stability in distribution is derived. The stabilizing effects of Markov chains, Brownian motions, and Poisson jumps are revealed. Based on these criteria, stabilization problems of stochastic differential equations with Markovian switching and Poisson jumps are developed.
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Impulsive stochastic functional differential equations with Markovian switching: study of exponential stability from a numerical solution point of view
Abstract This paper is devoted to the study of stochastic functional differential systems with Markov switching. It focuses on the stability of numerical solutions. To gain insight on how impulses, functional past dependence, random switching and stochastic disturbances can have impact on dynamic systems, this paper addresses exponential stability of the Euler–Maruyama approximations of stochastic functional differential equations with impulsive perturbations and Markovian switching. It begins with a presentation of the definitions of exponential stability in mean square and in the almost sure sense for stochastic functional differential equations with impulsive perturbations and Markovian switching. Then, it is devoted to showing that if the underlying system is stable in the aforementioned sense then the Euler–Maruyama approximation method faithfully reproduces exponential stability in the mean square and almost sure sense for sufficiently small step sizes and large iteration number. Two examples are provided to demonstrate the effectiveness of our results.
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- Award ID(s):
- 2229108
- PAR ID:
- 10591145
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- IMA Journal of Mathematical Control and Information
- Volume:
- 42
- Issue:
- 2
- ISSN:
- 0265-0754
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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