On a method of asymptotic expansions for infinite dimensional integrals with respect to smooth measures (Q2711774)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a method of asymptotic expansions for infinite dimensional integrals with respect to smooth measures |
scientific article |
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25 April 2001
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smooth measure
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logarithmic derivative
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Gaussian measure
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On a method of asymptotic expansions for infinite dimensional integrals with respect to smooth measures (English)
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The author obtains asymptotic expansions for integrals with respect to a smooth measure \(\mu\) on a Hilbert space. The integrals contain expressions like \(e^{W(\lambda,x)},\) where \(\lambda\) is a large parameter, and the phase function \(W\) has a special form involving the logarithmic gradient of \(\mu\). Several examples (in which \(\mu\) is a Gaussian measure) are studied in detail.
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