Multivalued backward stochastic differential equations with local lipschitz drift

• Published in: Stochastics and stochastics reports Vol. 60; no. 3-4; pp. 205 - 218
• Main Author: N'zi, Modeste
• Format: Journal Article
• Language: English
• Published: Abingdon Gordon and Breach Science Publishers 01.04.1997; Taylor & Francis
• Subjects: AMS 1991 Subject Classifications: 60H10, 60H20; Backward stochastic differential equations; convex function; Exact sciences and technology; Mathematics; maximal monotone operator; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Stochastic analysis; Brownian motion; Differential equation; Lipschitz drift; Maximal operator; Lipschitz function; Convex function; Delay equation; Stochastic equation
• ISSN: 1045-1129
• DOI: 10.1080/17442509708834106

We deal with a one dimensional multivalued backward stochastic differential equation associated to the subdifferential ∂hof a lower semi-continuous convex function h, with a local lipschitz coefficient (drift). When the terminal value is bounded, we prove the existence of a solution by using a suitable approximation of the drift by a double sequence of lipschitz functions. The uniqueness is obtained under the condition that the drift is local Lipschitz in y and globally Lipschitz in z. The existence result is an extension to the multivalued setting of the work of Hamadène