The transition from ergodic to explosive behavior in a family of stochastic differential equations (Q424484)
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scientific article; zbMATH DE number 6040292
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The transition from ergodic to explosive behavior in a family of stochastic differential equations |
scientific article; zbMATH DE number 6040292 |
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The transition from ergodic to explosive behavior in a family of stochastic differential equations (English)
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1 June 2012
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A specific parametrized family of two dimensional stochastic differential equations is considered. Regions of parameter space are identified where stability and existence of unique invariant probability distribution is assured on one hand, and where the process is unstable for some initial conditions with a strictly positive probability on the other. The proof in the former case uses construction of multiple Lyapunov functions constructed on a cover of the state space and for the degenerate case, the hypoellipticity property.
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stochastic differential equations
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stability
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instability
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Lyapunov functions
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unique invariant distribution
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