Stable convergence of multiple Wiener-Itô integrals
نویسندگان
چکیده
We prove sufficient conditions, ensuring that a sequence of multiple Wiener-Itô integrals (with respect to a general Gaussian process) converges stably to a mixture of normal distributions. Our key tool is an asymptotic decomposition of contraction kernels, realized by means of increasing families of projection operators. We also use an infinite-dimensional Clark-Ocone formula, as well as a version of the correspondence between “abstract” and “concrete” filtered Wiener spaces, in a spirit similar to Üstünel and Zakai (1997).
منابع مشابه
Convergence in variation of the joint laws of multiple Wiener–Itô integrals
The convergence in variation of the laws of multiple Wiener–Itô integrals with respect to their kernel has been studied by Davydov and Martynova in [1987. Limit behavior of multiple stochastic integral. Statistics and Control of Random Process (Preila, 1987), Nauka, Moscow, pp. 55–57 (in Russian)]. Here, we generalize this convergence for the joint laws of multiple Wiener–Itô integrals. In this...
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