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http://hdl.handle.net/2445/190527
Title: | On the strong convergence of multiple ordinary integrals to multiple Stratonovich integrals |
Author: | Bardina i Simorra, Xavier Rovira Escofet, Carles |
Keywords: | Processos gaussians Teoremes de límit (Teoria de probabilitats) Integrals estocàstiques Gaussian processes Limit theorems (Probability theory) Stochastic integrals |
Issue Date: | 2021 |
Publisher: | Universitat Autònoma de Barcelona |
Abstract: | Given $\left\{W^{(m)}(t), t \in[0, T]\right\}_{m \geq 1}$, a sequence of approximations to a standard Brownian motion $W$ in $[0, T]$ such that $W^{(m)}(t)$ converges almost surely to $W(t)$, we show that, under regular conditions on the approximations, the multiple ordinary integrals with respect to $d W^{(m)}$ converge to the multiple Stratonovich integral. We are integrating functions of the type $$ f\left(t_1, \ldots, t_n\right)=f_1\left(t_1\right) \cdots f_n\left(t_n\right) I_{\left\{t_1 \leq \cdots \leq t_n\right\}}, $$ where for each $i \in\{1, \ldots, n\}, f_i$ has continuous derivatives in $[0, T]$. We apply this result to approximations obtained from uniform transport processes. |
Note: | Reproducció del document publicat a: https://doi.org/10.5565/PUBLMAT6522114 |
It is part of: | Publicacions Matemàtiques, 2021, vol. 65, num. 2, p. 859-876 |
URI: | http://hdl.handle.net/2445/190527 |
Related resource: | https://doi.org/10.5565/PUBLMAT6522114 |
ISSN: | 0214-1493 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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