Uniqueness of strong solutions to stochastic differential equations in the plane with deterministic boundary process

James Juei-Chin Yeh

Vol. 128 (1987), No. 2, 391–400

DOI: 10.2140/pjm.1987.128.391

Abstract

Under the assumption of the existence of a weak solution and the pathwise uniqueness of solutions, existence and uniqueness of a strong solution to the stochastic differential system of non Markovian type in the plane

dXz	= α(z,X)dBz + β(z,X)dz for z ∈ R+2,
∂X	= x

is obtained where x is a continuous real valued function on ∂R₊²