| Issue |
ESAIM: COCV
Volume 28, 2022
|
|
|---|---|---|
| Article Number | 72 | |
| Number of page(s) | 26 | |
| DOI | https://doi.org/10.1051/cocv/2022062 | |
| Published online | 24 November 2022 | |
Stability in distribution and stabilization of switching jump diffusions*
1
Department of Applied Mathematics and Statistics, State University of New York - Korea Campus, Yeonsu-Gu, Incheon 21985, Korea
2
Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487, USA
3
Department of Mathematics, University of Connecticut, Storrs, CT 06269, USA
** Corresponding author: gyin@wayne.edu
Received:
20
April
2022
Accepted:
25
September
2022
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.
Mathematics Subject Classification: 34F05 / 60H10 / 60H20 / 60J60 / 93D15
Key words: Switching jump diffusion / stability in distribution / stabilization / Poisson process / Markov chain
The research of Ky Q. Tran was supported by the National Research Foundation of Korea Grant funded by the Korea Government (MIST) NRF-2021R1F1A1062361. The research of Dang H. Nguyen was supported in part by the National Science Foundation under grant DMS-1853467. The research of George Yin was supported in part by the National Science Foundation under grant DMS-2114649.
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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