On \(L^ p\) stochastic representations (Q1903164)
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scientific article; zbMATH DE number 820287
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On \(L^ p\) stochastic representations |
scientific article; zbMATH DE number 820287 |
Statements
On \(L^ p\) stochastic representations (English)
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22 April 1996
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The author proves the following integral representation result for stochastic integrals: Let \(w\) be a Brownian motion on \((\Omega, F^w, P)\). Then \(f \in L_p (F_\infty, P)\), \(1 < p < \infty\), has a representation as \(f = E |f |+ \int^\infty_0 Hdw\), where \(H \in L_p (dw)\), \(L_p (dw) : = \{H \in \wp\mid |H |_\infty < \infty\}\), \(|H |_p = |\int^\infty_0(H^2ds)^{1/2} |_{L_p}\). The representation is unique.
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Brownian motion
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stochastic \(p\)-integral representation
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stochastic integrals
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