Stochastic functional evolution equations with monotone nonlinearity: existence and stability of the mild solutions (Q2269632)
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| Language | Label | Description | Also known as |
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| English | Stochastic functional evolution equations with monotone nonlinearity: existence and stability of the mild solutions |
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Stochastic functional evolution equations with monotone nonlinearity: existence and stability of the mild solutions (English)
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17 March 2010
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The author studies existence, uniqueness and asymptotic stability of the mild solution of a stochastic functional evolution equation taking values in a separable Hilbert space. The equation is more general than those studied previously since the drift function is assumed to satisfy some demicontinuity and semimonotonicity (or one-sided Lipschitz) property rather than a global or local Lipschitz condition. The existence and uniqueness proof is based on a new Burkholder-type inequality
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Itô-type inequality
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Burkholder inequality
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demicontinuous
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semi-monotone
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mild solution
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asymptotic stability
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