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X: 16, 240-244, LNM 511 (1976)
YAMADA, Toshio
On the uniqueness of solutions of stochastic differential equations with reflecting barrier conditions (Stochastic calculus, 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 conditions
Comment: This extends to the reflecting barrier case the now classical result in the ``free'' case due to Yamada-Watanabe, J. Math. Kyoto Univ., 11, 1971. Many of these theorems have now simpler proofs using local times, in the spirit of Revuz-Yor, Continuous Martingales and Brownian Motion, Chapter IX
Keywords: Stochastic differential equations, Boundary reflection
Nature: Original
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