Williams, R. J.; Zheng, W. A.
On reflecting brownian motion - a weak convergence approach
Annales de l'I.H.P. Probabilités et statistiques, Tome 26 (1990) no. 3 , p. 461-488
Zbl 0704.60081 | 3 citations dans Numdam
URL stable : http://www.numdam.org/item?id=AIHPB_1990__26_3_461_0

Bibliographie

[1] R.F. Bass, P. Hsu, Some potential theory for reflecting Brownian motion in Hölder and Lipschitz domains, to appear in Ann. Prob.. Zbl 0732.60090

[2] R.F. Bass, P. Hsu, The semimartingale structure of reflecting Brownian motion, to appear in Proc. Am. Math. Soc. MR 1007487 | Zbl 0694.60075

[3] P. Billingsley, Convergence of Probability Measures, John Wiley and Sons, new York, 1968. MR 233396 | Zbl 0172.21201

[4] E. Carlen, Conservative diffusions, Comm. Math. Phys. 94, 293-316. MR 763381 | Zbl 0558.60059

[5] H. Federer, Geometric Measure Theory, Springer-Verlag, New York, 1969. MR 257325 | Zbl 0176.00801

[6] M. Fukushima, A construction of reflecting barrier Brownian motions for bounded domains, Osaka J. Math. 4 (1967), 183-215. MR 231444 | Zbl 0317.60033

[7] M. Fukushima, Dirichlet forms and Markov Processes, North-Holland, 1980. MR 569058 | Zbl 0422.31007

[8] E. Hewitt, K. Stromberg, Real and Abstract Analysis, Springer-Verlag, New York, 1965. MR 367121 | Zbl 0137.03202

[9] P. Hsu, Reflecting Brownian Motion, Boundary Local Time, and the Neumann Boundary Value Problem, Ph.D. Dissertation, Stanford, 1984.

[10] P.L. Lions, A.S. Sznitman, Stochastic differential equations with reflecting boundary conditions, Comm. Pure Appl. Math. 37 (1984), 511-537. MR 745330 | Zbl 0598.60060

[11] T.J. Lyons, W.A. Zheng, A crossing estimate for the canonical process on a Dirichlet space and a tightness result, Colloque Paul Levy sur les Processus Stochastiques, Asterisque, 157-158 (1988), 249-271. Zbl 0654.60059

[12] P.A. Meyer, W.A. Zheng, Tightness criteria for laws of semimartingales, Ann. Inst. Henri Poincaré, 20 (1984), N°4, 357-372. Numdam | MR 771895 | Zbl 0551.60046

[13] Y. Saisho, Stochastic differential equations for multi-dimensional domain with reflecting boundary, Prob. Theor. Rel. Fields, 74 (1987), 455-477. MR 873889 | Zbl 0591.60049

[14] E.M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, 1970. MR 290095 | Zbl 0207.13501

[15] D.W. Stroock, S.R.S. Varadhan, Diffusion processes with boundary conditions, Comm. Pure Appl. Math. 24 (1971), 147-225. MR 277037 | Zbl 0227.76131

[16] H. Tanaka, Stochastic differential equations with reflecting boundary conditions in convex regions, Hiroshima Math. J. 9 (1979), 163-177. MR 529332 | Zbl 0423.60055

[17] W.A. Zheng, Tightness results for laws of diffusion processes, Application to stochastic mechaniscs, Ann. Inst. Henri Poincaré 21 (1985), 103-124. Numdam | MR 798890 | Zbl 0579.60050

[18] W.A. Zheng, Semimartingales in predictable random open sets, Séminaire de Probabilités XVI, Lect. Notes Math. 920 (1982), Springer-Verlag, 370-379. Numdam | MR 658698 | Zbl 0481.60054