One-dimensional Stochastic Differential Equations with Generalized and Singular Drift
Abstract
Introducing certain singularities, we generalize the class of one-dimensional stochastic differential equations with so-called generalized drift. Equations with generalized drift, well-known in the literature, possess a drift that is described by the semimartingale local time of the unknown process integrated with respect to a locally finite signed measure \nu. The generalization which we deal with can be interpreted as allowing more general set functions \nu, for example signed measures which are only \sigma-finite. However, we use a different approach to describe the singular drift. For the considered class of one-dimensional stochastic differential equations, we derive necessary and sufficient conditions for existence and uniqueness in law of solutions.
Cite
@article{arxiv.1209.6159,
title = {One-dimensional Stochastic Differential Equations with Generalized and Singular Drift},
author = {Stefan Blei and Hans-Jürgen Engelbert},
journal= {arXiv preprint arXiv:1209.6159},
year = {2013}
}