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Taylor expansion of the density in a stochastic heat equation. (English) Zbl 0939.60067

A general result is proved on asymptotic expansions of densities for families of perturbed Wiener functionals following ideas developed by the authors. The general result is applied to a stochastic heat equation driven by space-time white noise and perturbed by a small parameter in the diffusion coefficient. The main theorem describes the asymptotic behaviour of the associated densities at a fixed point. The analysis is given in detail and it is recommended to mathematicians working in applications of Malliavin calculus.

MSC:

60H15 Stochastic partial differential equations (aspects of stochastic analysis)
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