Interchanging the order of differentiation and stochastic integration (Q801399)
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scientific article; zbMATH DE number 3878096
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Interchanging the order of differentiation and stochastic integration |
scientific article; zbMATH DE number 3878096 |
Statements
Interchanging the order of differentiation and stochastic integration (English)
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1984
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Let \(\{M_ t,f_ t\}_{0\leq t\leq T}\) be a locally square-integrable martingale, and suppose that \(\{f(t,\theta,\omega)\}\) is a family of random variables, under some conditions, the authors prove that \(\frac{d}{d\theta} \int^{T}_{0}f(t,\theta,\omega)dM_ t = \int^{T}_{0} \frac{d}{d\theta} f(t,\theta,\omega)dM_ t\).
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differentiation with respect to a parameter
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