On the convergence to the multiple Wiener-Itô integral |
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Authors: | Xavier Bardina Maria Jolis |
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Institution: | a Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193-Bellaterra (Barcelona), Spain b SAMOS/MATISSE, Centre d'Economie de La Sorbonne, Université de Panthéon-Sorbonne Paris 1, 90, rue de Tolbiac, 75634 Paris Cedex 13, France |
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Abstract: | We study the convergence to the multiple Wiener-Itô integral from processes with absolutely continuous paths. More precisely, consider a family of processes, with paths in the Cameron-Martin space, that converges weakly to a standard Brownian motion in C0(0,T]). Using these processes, we construct a family that converges weakly, in the sense of the finite dimensional distributions, to the multiple Wiener-Itô integral process of a function f∈L2(n0,T]). We prove also the weak convergence in the space C0(0,T]) to the second-order integral for two important families of processes that converge to a standard Brownian motion. |
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Keywords: | 60B10 60F05 60H05 |
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