# name
On the strong convergence of multiple ordinary integrals to multiple Stratonovich integrals

# metadata.dc.description.abstract[].value
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.

# metadata.dc.rights[].value
(c) Universitat Autònoma de Barcelona, 2021

# metadata.dc.source[].value
Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.subject.classification[].value
Teoremes de límit (Teoria de probabilitats)

# metadata.dc.title[].value
On the strong convergence of multiple ordinary integrals to multiple Stratonovich integrals