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arXiv · 1209.6159

One-dimensional Stochastic Differential Equations with Generalized and Singular Drift

Stefan Blei·Hans-Jürgen Engelbert
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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 ν. The generalization which we deal with can be interpreted as allowing more general set functions ν, for example signed measures which are only σ-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.

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Stefan Blei, Hans-Jürgen Engelbert. 2012-09-27. One-dimensional Stochastic Differential Equations with Generalized and Singular Drift. https://doi.org/10.1016/j.spa.2013.06.014

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