6 citations · 6 across the 5 of their papers we have counts for
7 papers
Optimal approximation of anticipating SDEs
Peter Parczewski
We derive the optimal rate of convergence for the mean squared error at the terminal point for anticipating linear stochastic differential equations, where the integral is interpre…
Extensions of the Hitsuda-Skorokhod integral
Peter Parczewski
We present alternative definitions of the stochastic integral introduced by Ayew and Kuo and of the Hitsuda-Skorokhod integral extended to domains in -spaces, . Our…
Optimal approximation of Skorohod integrals - examples with substandard rates
Peter Parczewski
We consider optimal approximation with respect to the mean square error of Itô integrals and Skorohod integrals given an equidistant discretization of the Brownian motion. We obtai…
Optimal approximation of Skorohod integrals
Andreas Neuenkirch, Peter Parczewski
In this manuscript, we determine the optimal approximation rate for Skorohod integrals of sufficiently regular integrands. This generalizes the optimal approximation results for It…
The self-normalized Donsker theorem revisited
Peter Parczewski
We extend the Poincaré--Borel lemma to a weak approximation of a Brownian motion via simple functionals of uniform distributions on n-spheres in the Skorokhod space . Thi…
Discretizing Malliavin calculus
Christian Bender, Peter Parczewski
Suppose is a Brownian motion and is an approximating sequence of rescaled random walks on the same probability space converging to pointwise in probability. We provid…