Mean square characterisation of a stochastic Volterra integrodifferential equation with delay (Q2113747)
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scientific article; zbMATH DE number 7488803
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Mean square characterisation of a stochastic Volterra integrodifferential equation with delay |
scientific article; zbMATH DE number 7488803 |
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Mean square characterisation of a stochastic Volterra integrodifferential equation with delay (English)
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14 March 2022
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Summary: In this paper the asymptotic behaviour of the mean square of the solution of a linear stochastic Volterra integro-differential equation with delay is entirely characterised. In the case when the solution is mean-square asymptotically stable or unstable the exact rate of growth or decay can be determined by the real solution of a transcendental equation which is constructed as a by-product of the proof. The proof of the mean square stability of an equation with fading memory is also sketched.
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stochastic functional differential equations
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stochastic Volterra equation
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mean square stability
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characteristic equation
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characteristic exponent
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renewal equation
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exponential stability
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variation of constants formula
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