A uniqueness and smoothness result for multidimensional SDE’s on the plane with nondecreasing coefficient
Document Type
Lecture
Publication Date
2-23-2023
Abstract
In this talk, we discuss the path by path uniqueness for multidimensional stochastic differentialequations driven by the Brownian sheet. We assume that the drift coefficient is unbounded, ver-ifies a spacial linear growth condition and is componentwise nondeacreasing. We first show theresult for bounded and measurable drift. Our proofs rely on a local time-space representation ofBrownian sheet and a type of law of the iterated logarithm for the Brownian sheet. The result inthe unbounded case then follows by using the Gronwall’s lemma on the plane. Under boundednessof the solution, we also prove that the obtained solution is Malliavin smooth.This talk is based on a joint work with A. M. Bogso and M. Dieye.
Relational Format
presentation
Recommended Citation
Pamen, Olivier Menoukeu, "A uniqueness and smoothness result for multidimensional SDE’s on the plane with nondecreasing coefficient" (2023). Probability & Statistics Seminar. 21.
https://egrove.olemiss.edu/math_statistics/21
