Vol. 13, No. 3, 2020

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Uniqueness of a three-dimensional stochastic differential equation

Carl Mueller and Giang Truong

Vol. 13 (2020), No. 3, 433–444
Abstract

In order to extend the study of the uniqueness property of multidimensional systems of stochastic differential equations, we look at the following three-dimensional system of equations, of which the two-dimensional case has been well studied: dXt = Y tdt, dY t = Ztdt, dZt = |Xt|αdBt. We prove that if (X0,Y 0,Z0)(0,0,0) and 3 4 < α < 1, then the system of equations has a unique solution in the strong sense.

Keywords
white noise, stochastic differential equations, uniqueness
Mathematical Subject Classification 2010
Primary: 60H10
Secondary: 34F05
Milestones
Received: 3 October 2019
Revised: 18 February 2020
Accepted: 23 May 2020
Published: 14 July 2020

Communicated by Amarjit Singh Budhiraja
Authors
Carl Mueller
Department of Mathematics
University of Rochester
Rochester, NY
United States
Giang Truong
Department of Mathematics
University of Rochester
Rochester, NY
United States