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Applied Mathematics Letters
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Qingyan Meng +3 more
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Qingyan Meng +3 more
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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
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Zilong Zhang, Quanxin Zhu
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Zilong Zhang, Quanxin Zhu
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The pth moment exponential ultimate boundedness of impulsive stochastic differential systems
Applied Mathematics Letters, 2015Shuzhi Sam Ge, Liguang Xu
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Ultimate boundedness of impulsive fractional differential equations
Applied Mathematics Letters, 2016Liguang Xu, Hu Hongxiao
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