A uniqueness result of multidimensional SDE's on the plane with nondecreasing coefficients

This talk will be given by Olivier Menoukeu Pamen (University of Liverpool)

Abstract: In this talk, we discuss a uniqueness result (in the sense of Davie 07) for multidimensional stochastic differential equations driven by the Brownian sheet. We assume that the drift coefficient is unbounded, verifies a spacial linear growth condition and is componentwise nondeacreasing. We first show the result when the drift is bounded measurable and nondecreasing. Our proofs rely on a local time-space representation of Brownian sheet and a type of law of the iterated logarithm for the Brownian sheet. The result in the unbounded case then follows by using the Gronwall’s lemma on the plane. 

This talk is based on a joint work with A. M. Bogso and M. Dieye.

Keywords: Brownian sheet, SDEs on the plane, path by path uniqueness, local time.

If you are interested in joining this talk, please contact Dr Konstantinos Dareiotis at k.dareiotis@leeds.ac.uk for the Zoom details.