\(J\)-convergence of switching processes with rare perturbations to diffusion processes with Poisson type jumps (Q2726254)
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scientific article; zbMATH DE number 1620692
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(J\)-convergence of switching processes with rare perturbations to diffusion processes with Poisson type jumps |
scientific article; zbMATH DE number 1620692 |
Statements
16 July 2001
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\(J\)-convergence
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Skorokhod space
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switching process
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Markov process
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stochastic differential equation
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diffusion process
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Poisson process
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aggregation
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\(J\)-convergence of switching processes with rare perturbations to diffusion processes with Poisson type jumps (English)
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Skorokhod's notion of \(J\)-topology introduced in 1956 stimulated new researches in studying functional convergence to discontinuous processes in Skorokhod space \(D.\) \(J\)-convergence of trajectories for a special subclass of switching processes is studied: recurrent processes of semi-Markov type with both rare interference of chance and asymptotically aggregated external Markov environment. As a class of limiting processes solutions of differential and stochastic differential equations with Poisson switches are obtained. The results presented in the paper give in some sense a connection between cases of ``rare'' and ``fast'' switches.NEWLINENEWLINEFor the entire collection see [Zbl 0956.00022].
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