A stochastic characterization of Hermite polynomials (Q1269988)
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scientific article; zbMATH DE number 1213225
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A stochastic characterization of Hermite polynomials |
scientific article; zbMATH DE number 1213225 |
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A stochastic characterization of Hermite polynomials (English)
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24 November 1998
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The authors characterize Hermite polynomials by the following property: Let \(h_n\) be an analytic function on the real numbers, such that \(E(h_n(U_t)\mid W_s)=(s/t)^{n/2}h_n(U_s)\), for \(U_t=t^{-1/2}W_t\), where \(W_t\) is a standard Brownian motion. Then \(h_n\) is a Hermite polynomial up to a constant.
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Hermite polynomials
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