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math.PR2017★ 3 cited
Two quadrature rules for stochastic Itô-integrals with fractional Sobolev regularity
Monika Eisenmann, Raphael Kruse
In this paper we study the numerical quadrature of a stochastic integral, where the temporal regularity of the integrand is measured in the fractional Sobolev-Slobodeckij norm in $…
math.PR2016★ 17 cited
A discrete stochastic Gronwall Lemma
Raphael Kruse, Michael Scheutzow
We derive a discrete version of the stochastic Gronwall Lemma found in [Scheutzow, IDAQP, 2013]. The proof is based on a corresponding deterministic version of the discrete Gronwal…
math.PR2013★ 47 cited
Duality in refined Sobolev-Malliavin spaces and weak approximations of SPDE
Adam Andersson, Raphael Kruse, Stig Larsson
We introduce a new family of refined Sobolev-Malliavin spaces that capture the integrability in time of the Malliavin derivative. We consider duality in these spaces and derive a B…