Wong-Zakai type convergence in infinite dimensions
Arnab Ganguly
TL;DR
This paper extends Wong-Zakai convergence results to infinite-dimensional stochastic differential equations driven by Hilbert-space valued semimartingales, providing general correction factors and approximation examples.
Contribution
It generalizes Wong-Zakai convergence to infinite dimensions and derives a universal correction factor for such stochastic equations.
Findings
Established convergence of solutions for infinite-dimensional SDEs.
Derived a general correction factor for Wong-Zakai approximations.
Provided examples illustrating the application of the theorems.
Abstract
The paper deals with convergence of solutions of a class of stochastic differential equations driven by infinite-dimensional semimartingales. The infinite-dimensional semimartingales considered in the paper are Hilbert-space valued. The theorems presented generalize the convergence result obtained by Wong and Zakai for stochastic differential equations driven by linear interpolations of a finite-dimensional Brownian motion. In particular, a general form of the correction factor is derived. Examples are given illustrating the use of the theorems to obtain other kinds of approximation results.
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Taxonomy
TopicsStochastic processes and financial applications · Nonlinear Differential Equations Analysis · Stochastic processes and statistical mechanics