On the strong convergence of multiple ordinary integrals to multiple Stratonovich integrals
- 1 July 2021
- journal article
- research article
- Published by Universitat Autonoma de Barcelona in Publicacions Matemàtiques
- Vol. 65 (2), 859-876
- https://doi.org/10.5565/publmat6522114
Abstract
Given {W-(m) (t), t is an element of [0, T]}(m>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 dW((m)) converge to the multiple Stratonovich integral. We are integrating functions of the type f(t(1), ..., t(n)) - f(1)(t(1)) ... f(n)(t(n))I-{t1 <= ... <= tn}, where for each i is an element of {1, ..., n}, f(i) has continuous derivatives in [0, T]. We apply this result to approximations obtained from uniform transport processes.Keywords
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