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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/190527
On the strong convergence of multiple ordinary integrals to multiple Stratonovich integrals
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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.
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BARDINA I SIMORRA, Xavier and ROVIRA ESCOFET, Carles. On the strong convergence of multiple ordinary integrals to multiple Stratonovich integrals. Publicacions Matemàtiques. 2021. Vol. 65, num. 2, pags. 859-876. ISSN 0214-1493. [consulted: 7 of August of 2026]. Available at: https://hdl.handle.net/2445/190527