Cranston, Michael; Le Jan, Yves Noncoalescence for the Skorohod equation in a convex domain of \({\mathbb{R}}^ 2\). (English) Zbl 0695.60056 Probab. Theory Relat. Fields 87, No. 2, 241-252 (1990). Given a convex domain of \({\mathbb{R}}^ 2\), we show that a.s. the paths of two solutions of the Skorokhod equations driven by the same Brownian motion but starting at different points do not meet at the same time. Cited in 10 Documents MSC: 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) Keywords:local time; time change; reflected Brownian motion; Skorokhod equations PDFBibTeX XMLCite \textit{M. Cranston} and \textit{Y. Le Jan}, Probab. Theory Relat. Fields 87, No. 2, 241--252 (1990; Zbl 0695.60056) Full Text: DOI References: [1] Anderson, R.; Orey, S., Small random perturbation of dynamical systems with reflecting boundary, Nagoya Math. J., 60, 189-216 (1976) · Zbl 0324.60063 [2] Bensoussan, A.; Lions, J. L.; Pinsky, M. A., Diffusion processes in bounded domains, Probabilistic methods in differential equations, 8-25 (1974), Berlin Heidelberg New York: Springer, Berlin Heidelberg New York [3] Cranston, M.; Le Jan, Y., On the non coalescence of a two point Brownian motion reflecting on a circle, Ann. Inst. Poincaré, 25, 99-107 (1989) · Zbl 0679.60080 [4] Doss, H.; Priouret, P., Support d’un processus de réflexion. Z. Wahrscheinlichkeitstheor, Verw. Geb., 61, 327-345 (1982) · Zbl 0499.60083 [5] Lyons, P. L.; Sznitman, A. S., Equations with reflecting boundary conditions, C.P.A.M., XXXVII, 511-537 (1984) · Zbl 0598.60060 [6] Tanaka, H., Stochastic differential equations with reflecting boundary condition in convex regions, Hiroshima Math. J., 9, 163-177 (1979) · Zbl 0423.60055 [7] Weerasinghe, A.: Some properties of reflected Brownian motion. Ph. D. Thesis, University of Minnesota 1985 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.