Stability in distribution and stabilization of switching jump diffusions
ESAIM: Control, Optimisation and Calculus of Variations, Tome 28 (2022), article no. 72

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.

DOI : 10.1051/cocv/2022062
Classification : 34F05, 60H10, 60H20, 60J60, 93D15
Keywords: Switching jump diffusion, stability in distribution, stabilization, Poisson process, Markov chain 
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     author = {Tran, Ky Q. and Nguyen, Dang H. and Yin, George},
     title = {Stability in distribution and stabilization of switching jump diffusions},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     year = {2022},
     publisher = {EDP-Sciences},
     volume = {28},
     doi = {10.1051/cocv/2022062},
     mrnumber = {4513263},
     zbl = {1515.60215},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/cocv/2022062/}
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Tran, Ky Q.; Nguyen, Dang H.; Yin, George. Stability in distribution and stabilization of switching jump diffusions. ESAIM: Control, Optimisation and Calculus of Variations, Tome 28 (2022), article no. 72. doi: 10.1051/cocv/2022062

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Cité par Sources :

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.