Almost sure polynomial stability and stabilization of stochastic differential systems with impulsive effects

Article Mathematics, Applied

POLYNOMIAL STABILITY OF STOCHASTIC HEAT EQUATIONS

Guangying Lv et al.

Summary: In this paper, the long time behavior of stochastic heat equations is considered, with a focus on polynomial stability. Sufficient conditions are provided to ensure stability. Results indicate that noise (time diffusion) prevents the solutions from decaying in p-th moment, which is consistent with the nature of noise as a diffusion process. However, the partial diffusion operator (spatial diffusion) accelerates the decay of solutions.

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS (2023)

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Article Mathematics, Applied

Long time behavior of stochastic Mckean-Vlasov equations

Guangying Lv et al.

Summary: This short paper discusses the long time behavior of stochastic Mckean-Vlasov equations, considering the exponential, polynomial, and logarithmic decay. Sufficient conditions are provided to obtain these exponents.

APPLIED MATHEMATICS LETTERS (2022)

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Article Automation & Control Systems

Exponential stability of impulsive stochastic differential equations with Markovian switching

Ky Q. Tran et al.

Summary: This paper investigates moment exponential stability of a class of Markovian switching stochastic differential equations with impulsive perturbations. Explicit criteria for stability and instability are derived, and the contributions of Markovian switching and impulsive perturbations to stability and instability are revealed.

SYSTEMS & CONTROL LETTERS (2022)

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Article Automation & Control Systems

Stability of stochastic differential equations driven by the time-changed Levy process with impulsive effects

Xiuwei Yin et al.

Summary: This paper discusses the stability of nonlinear stochastic differential equations driven by time-changed Levy process with impulsive effects. Some sufficient conditions are provided to ensure stability in different senses. The efficiency of the results is illustrated through numerical simulations in some examples.

INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE (2021)

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Article Mathematics, Applied

Polynomial stability of highly non-linear time-changed stochastic differential equations

Wei Liu

Summary: This study investigates the moment stability of a class of time-changed stochastic differential equations with coefficients allowed to grow super-linearly. It is shown that the decay rate is polynomial for certain types of subordinators, which differs significantly from classical SDEs driven by Brownian motion.

APPLIED MATHEMATICS LETTERS (2021)

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Article Automation & Control Systems