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Pathwise solvability of stochastic integral equations with generalized drift and non-smooth dispersion functions

Karatzas, Ioannis and Ruf, Johannes (2016) Pathwise solvability of stochastic integral equations with generalized drift and non-smooth dispersion functions. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 52 (2). pp. 915-938. ISSN 0246-0203

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Identification Number: 10.1214/14-AIHP660

Abstract

We study one-dimensional stochastic integral equations with non-smooth dispersion coëfficients, and with drift components that are not restricted to be absolutely continuous with respect to Lebesgue measure. In the spirit of Lamperti, Doss and Sussmann, we relate solutions of such equations to solutions of certain ordinary integral equations, indexed by a generic element of the underlying probability space. This relation allows us to solve the stochastic integral equations in a pathwise sense.

Item Type: Article
Official URL: http://www.imstat.org/aihp
Additional Information: © 2016 Association des Publications de l’Institut Henri Poincaré
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Sets: Departments > Mathematics
Date Deposited: 11 Oct 2017 09:20
Last Modified: 20 May 2019 02:12
URI: http://eprints.lse.ac.uk/id/eprint/84573

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