On the general decay stability of stochastic differential equations with unbounded delay (Q2890879)
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scientific article; zbMATH DE number 6045507
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the general decay stability of stochastic differential equations with unbounded delay |
scientific article; zbMATH DE number 6045507 |
Statements
12 June 2012
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stochastic delay differential equation
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unbounded delay
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Razumikhin-type theorem
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stability
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\(M\)-matrix
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0.9693488
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0.9651909
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0.95754355
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0.9378802
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0.9365102
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0.9360322
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0.9344089
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0.9340648
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On the general decay stability of stochastic differential equations with unbounded delay (English)
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Razumikhin-type theorems are proved for establishing moment stability and almost sure stability of solutions of nonlinear stochastic differential equations with unbounded delay of the form NEWLINE\[NEWLINEdx(t)= f(t,x(t), y(t))\,dt+ g(t,x(t), y(t))\,dw(t),NEWLINE\]NEWLINE where \(y(t)= x(t-\delta(t))\), \(\delta(t)\in C^1(\mathbb{R}_+, \mathbb{R}_+)\), and \(w(t)\) is an \(m\)-dimensional Brownian motion. \(M\)-matrix theory is used to develop more easily implemented versions of these theorems. Use of the theorems is demonstrated with a couple of examples.
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