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Ultimate boundedness and weak recurrence of stochastic evolution equations
Stochastic Analysis and Applications, 1999We study the weak recurrence and weakly positive recurrence properties to compact sets for the strong solutions of stochastic evolution equations.
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Journal of the London Mathematical Society, 2000
Summary: Consider the following infinite-dimensional stochastic evolution equation over some Hilbert space \(H\) with norm \(|\cdot |\): \[ X_t=x_0+ \int^t_0 f(X_s,s)ds +\int^t_0 g(X_s,s)dW_s, \quad t\geq 0,\;P\text{ almost surely}. \] It is proved that under certain mild assumptions, the strong solution \(X_t(x_0)\in V\hookrightarrow H\hookrightarrow ...
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Summary: Consider the following infinite-dimensional stochastic evolution equation over some Hilbert space \(H\) with norm \(|\cdot |\): \[ X_t=x_0+ \int^t_0 f(X_s,s)ds +\int^t_0 g(X_s,s)dW_s, \quad t\geq 0,\;P\text{ almost surely}. \] It is proved that under certain mild assumptions, the strong solution \(X_t(x_0)\in V\hookrightarrow H\hookrightarrow ...
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Stochastic Analysis and Applications, 2000
In this paper, we establish the Lyapunov function characterization which is a sufficient and necessary condition for mild solutions of semilinear stochastic evolution equations to be exponentially stable in mean square. We also study the Lyapunov function characterization of ultimate exponential boundedness, a concept which is closely related to the ...
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In this paper, we establish the Lyapunov function characterization which is a sufficient and necessary condition for mild solutions of semilinear stochastic evolution equations to be exponentially stable in mean square. We also study the Lyapunov function characterization of ultimate exponential boundedness, a concept which is closely related to the ...
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Communications in Nonlinear Science and Numerical Simulation
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zilong Zhang, Quanxin Zhu
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zilong Zhang, Quanxin Zhu
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Boundedness analysis of stochastic pantograph differential systems
Applied Mathematics Letters, 2021Liguang Xu, Hu Hongxiao
exaly
Exponential ultimate boundedness and stability of stochastic differential equations with impulese
Asian Journal of Control, 2023Jianli Li
exaly