A criterion for invariant measures of Itô processes based on the symbol (Q2515514)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A criterion for invariant measures of Itô processes based on the symbol |
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A criterion for invariant measures of Itô processes based on the symbol (English)
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5 August 2015
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The purpose of this paper is to show that for an Itō process \(X\) with symbol \(p(x, \xi)\) the equation \[ \int e^{i, x, \xi}p(x, \xi)\mu(dx)=0 \] holds if (and only if) \(\mu\) is an (infinitesimal) invariant law for \(X\). It should be noted that in this new criterion no test functions are needed.
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Itō process
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invariant measure
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symbol
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stochastic differential equation
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