One-dimensional stochastic differential equations with generalized and singular drift

Stefan Blei and Hans-Jürgen Engelbert

Stochastic Processes and their Applications, 2013, vol. 123, issue 12, 4337-4372

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.

Keywords: Singular stochastic differential equations; Local times; Generalized drift; Singular drift; Uniqueness in law; Space transformation; Bessel process; Bessel equation (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:123:y:2013:i:12:p:4337-4372

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DOI: 10.1016/j.spa.2013.06.014

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