On pathwise uniqueness for Brownian motion in a quadrant with oblique reflection

• 成果类型: Article
• 署名作者: Bass, Richard F.; Burdzy, Krzysztof
• 署名单位: University of Connecticut; University of Washington; University of Washington Seattle
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051; 1432-2064
• DOI: 10.1007/s00440-025-01457-7
• 发表日期: 2026-04
• 页码: 1397-1442
• 关键词: Existence; wedge

摘要

Consider the deterministic Skorokhod equation in the closed first quadrant: X-t=x(0)+f(t)+integral(t)(0)v(X-s)dL(s), where f:[0,infinity)-> R-2 is a continuous function, f(0)=0, X-t takes values in the quadrant for all t, and L-t is a process that starts at 0, is non-decreasing and continuous, and increases only at those times when is on the boundary of the quadrant. Suppose v on the positive x axis, equals (1,-a(2)) on the positive y axis, and v(0) points into the closed first quadrant. Let theta(i)=arctan a(i), i=1,2. Suppose that theta(1)+theta(2)-theta(2)>0, |a(1)a(2)|>1 and log|a(1)|+log|a(2)| / a(1)+a(2) > pi/2. We prove that for almost every trajectory of standard 2-dimensional Brownian motion B-t, the Skorokhod equation with f(t)equivalent to B-t has at least two solutions.