Strong Uniqueness of Singular Stochastic Delay Equations
Abstract
In this article we introduce a new method for the construction of unique strong solutions of a larger class of stochastic delay equations driven by a discontinuous drift vector field and a Wiener process. The results obtained in this paper can be regarded as an infinite-dimensional generalization of those of A. Y. Veretennikov [42] in the case of certain stochastic delay equations with irregular drift coefficients. The approach proposed in this work rests on Malliavin calculus and arguments of a "local time variational calculus", which may also be used to study other types of stochastic equations as e.g. functional It\^{o}-stochastic differential equations in connection with path-dependent Kolmogorov equations [15].
Cite
@article{arxiv.1707.02271,
title = {Strong Uniqueness of Singular Stochastic Delay Equations},
author = {D. Baños and H. H. Haferkorn and F. Proske},
journal= {arXiv preprint arXiv:1707.02271},
year = {2017}
}
Comments
68 pages, 0 figures; Fixes incorrect assumption (T) that is necessary for the proof of Lemma 3.9; more space efficient writing of equations; additional Remark 2.5 on strong local non-determinism; other minor corrections such as typos, acknowledgements and references