Markov processes associated with \(L^{p}\)-resolvents and applications to stochastic differential equations on Hilbert space (Q871613)
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scientific article; zbMATH DE number 5134740
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Markov processes associated with \(L^{p}\)-resolvents and applications to stochastic differential equations on Hilbert space |
scientific article; zbMATH DE number 5134740 |
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Markov processes associated with \(L^{p}\)-resolvents and applications to stochastic differential equations on Hilbert space (English)
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20 March 2007
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Let \(E\) be a Lusin topological space, \(p\geq 1\) and \(\mu\) a \(\sigma\)-finite measure on \(E\). A general condition is given on the generator of a \(C_0\)-semigroup on \(L^p(E,\mu)\) so that it generates a sufficiently regular Markov process on \(E\). Applications of the main result are carefully discussed. In particular, martingale solutions to stochastic differential equations on Hilbert spaces are studied.
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\(L^p\)-resolvents
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right processes
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invariant measures
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Lyapunov functions
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