Path-by-path uniqueness of multidimensional SDE's on the plane with nondecreasing coefficients

Autor:	Bogso, Antoine-Marie, Dieye, Moustapha, Menoukeu-Pamen, Olivier
Rok vydání:	2021
Předmět:	Mathematics - Probability 60H05 60H15
Zdroj:	Electron. J. Probab. 27: 1-26 (2022)
Druh dokumentu:	Working Paper
DOI:	10.1214/22-EJP844
Popis:	In this paper we study path-by-path uniqueness for multidimensional stochastic differential equations driven by the Brownian sheet. We assume that the drift coefficient is unbounded, verifies a spatial linear growth condition and is componentwise nondeacreasing. Our approach consists of showing the result for bounded and componentwise nondecreasing drift using both a local time-space representation and a law of iterated logarithm for Brownian sheets. The desired result follows using a Gronwall type lemma on the plane. As a by product, we obtain the existence of a unique strong solution of multidimensional SDEs driven by the Brownian sheet when the drift is non-decreasing and satisfies a spatial linear growth condition. Comment: 24 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2112.00393 Zobrazit plný text záznamu View this record from Arxiv