: 16, 240-244, LNM 511 (1976)YAMADA, Toshio
On the uniqueness of solutions of stochastic differential equations with reflecting barrier conditions
, Diffusion theory
A stochastic differential equation is considered on the positive half-line, driven by Brownian motion, with time-dependent coefficients and a reflecting barrier condition at $0$ (Skorohod style). Skorohod proved pathwise uniqueness under Lipschitz condition, and this is extended here to moduli of continuity satisfying integral conditionsComment:
This extends to the reflecting barrier case the now classical result in the ``free'' case due to Yamada-Watanabe, J. Math. Kyoto Univ.
, 1971. Many of these theorems have now simpler proofs using local times, in the spirit of Revuz-Yor, Continuous Martingales and Brownian Motion,
Chapter IXKeywords: Stochastic differential equations
, Boundary reflectionNature: Original Retrieve article from Numdam