Generalized ornstein-uhlenbeck process having a characteristic operator with polynomial coefficients |
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Authors: | Itaru Mitoma |
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Institution: | (1) Department of Mathematics, Hokkaido University, 060 Sapporo, Japan |
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Abstract: | Summary Let be a weighted Schwartz's space of rapidly decreasing functions, ![PHgr](/content/ju3hv47771892517/xxlarge934.gif) the dual space and (t) a perturbed diffusion operator with polynomial coefficients from into itself. It is proven that (t) generates the Kolmogorov evolution operator from into itself via stochastic method. As applications, we construct a unique solution of a Langevin's equation on ![PHgr](/content/ju3hv47771892517/xxlarge934.gif) : whereW(t) is a ![PHgr](/content/ju3hv47771892517/xxlarge934.gif) Brownian motion and *(t) is the adjoint of (t) and show a central limit theorem for interacting multiplicative diffusions. |
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