IX: 35, 534-554, LNM 465 (1975)
EL KAROUI, Nicole
Processus de réflexion dans ${\bf R}^n$ (Diffusion theory)
In the line of the seminar on diffusions 419 this talk presents the theory of diffusions in a half space with continuous coefficients and a boundary condition on the boundary hyperplane involving a reflexion part, but more general than the pure reflexion case considered by Stroock-Varadhan (Comm. Pure Appl. Math., 24, 1971). The point of view is that of martingale problems
Comment: This talk is a late publication of work done by the author in 1971
Keywords: Boundary reflection, Local times
Nature: Original
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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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