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 reflectionNature: Original
Retrieve article from Numdam
XII: 13, 114-131, LNM 649 (1978)
YAMADA, Toshio
Sur une construction des solutions d'équations différentielles stochastiques dans le cas non-lipschitzien (
Stochastic calculus)
The results of this paper improve on those of the author's paper (
Zeit. für W-theorie, 36, 1976) concerning a one-dimensional stochastic differential equations of the classical Ito type, whose coefficients satisfy a Hölder-like condition instead of the standard Lipschitz condition. The proofs are simplified, and strong convergence of the Cauchy method is shown
Comment: Such equations play an important role in the theory of Bessel processes (see chapter XI of Revuz-Yor,
Continuous Martingales and Brownian Motion, Springer 1999
Keywords: Stochastic differential equations,
Hölder conditionsNature: Original Retrieve article from Numdam
XVI: 38, 412-441, LNM 920 (1982)
KAWABATA, Shigetoku;
YAMADA, Toshio
On some limit theorems for solutions of stochastic differential equations Retrieve article from Numdam
XXV: 13, 121-137, LNM 1485 (1991)
KAWABATA, Shigetoku;
YAMADA, Toshio
On Newton's method for stochastic differential equations Retrieve article from Numdam
