An \(\infty\)-dimensional inhomogeneous Langevin's equation (Q1067304)
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scientific article; zbMATH DE number 3928022
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An \(\infty\)-dimensional inhomogeneous Langevin's equation |
scientific article; zbMATH DE number 3928022 |
Statements
An \(\infty\)-dimensional inhomogeneous Langevin's equation (English)
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1985
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Let \(\Phi\) be a weighted Schwartz's space of rapidly decreasing functions, \(\Phi\) ' the dual space, W(t) a \(\Phi\) '-valued Brownian motion, L(t) a perturbed diffusion operator from \(\Phi\) into itself and \(L^*(t)\) the adjoint of L(t). The aim of this paper is to construct a unique solution of a Langevin's equation: \(dX(t)=dW(t)+L^*(t)X(t)dt\) and as an application to prove a central limit theorem for the McKean diffusions.
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weighted Schwartz's space of rapidly decreasing functions
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Langevin's equation
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central limit theorem
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