The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off


  1. Airault, HÈlËne. Perturbations singuliËres et solutions stochastiques de problËmes de D. Neumann-Spencer. (French) J. Math. Pures Appl. (9) 55 (1976), no. 3, 233--267. MR0501184 (58 #18606)

  1. Anderson, Robert F.; Orey, Steven. Small random perturbation of dynamical systems with reflecting boundary. Nagoya Math. J. 60 (1976), 189--216. MR0397893 (53 #1749)

  1. Andres, Sebastian. Pathwise differentiability for SDEs in a convex polyhedron with oblique reflection. Ann. Inst. Henri PoincarÈ Probab. Stat. 45 (2009), no. 1, 104--116. MR2500230 (2010e:60118)

  1. Burdzy, Krzysztof. Differentiability of stochastic flow of reflected Brownian motions. Electron. J. Probab. 14 (2009), no. 75, 2182--2240. MR2550297 (2011b:60321)

  1. Burdzy, Krzysztof; Chen, Zhen-Qing. Coalescence of synchronous couplings. Probab. Theory Related Fields 123 (2002), no. 4, 553--578. MR1921013 (2003e:60184)

  1. Burdzy, Krzysztof; Chen, Zhen-Qing; Jones, Peter. Synchronous couplings of reflected Brownian motions in smooth domains. Illinois J. Math. 50 (2006), no. 1-4, 189--268 (electronic). MR2247829 (2007i:60102)

  2. Burdzy, Krzysztof; Lee, John M. Multiplicative functional for reflected Brownian motion via deterministic ODE. Preprint, Math. Review number not available.

  1. Cranston, M.; Le Jan, Y. On the noncoalescence of a two point Brownian motion reflecting on a circle. Ann. Inst. H. PoincarÈ Probab. Statist. 25 (1989), no. 2, 99--107. MR1001020 (90k:60154)

  1. Cranston, M.; Le Jan, Y. Noncoalescence for the Skorohod equation in a convex domain of R2. Probab. Theory Related Fields 87 (1990), no. 2, 241--252. MR1080491 (92e:60116)

  1. Denisov, I.-V.  A random walk and a Wiener process near a maximum. Theor. Prob. Appl. 28 (1984), 821--824.  Math. Review number not available.

  1. Deuschel, Jean-Dominique; Zambotti, Lorenzo. Bismut-Elworthy's formula and random walk representation for SDEs with reflection. Stochastic Process. Appl. 115 (2005), no. 6, 907--925. MR2134484 (2006e:60080)

  1. Hsu, Elton P. Multiplicative functional for the heat equation on manifolds with boundary. Michigan Math. J. 50 (2002), no. 2, 351--367. MR1914069 (2003f:58067)

  1. Ikeda, Nobuyuki; Watanabe, Shinzo. Stochastic differential equations and diffusion processes. North-Holland Mathematical Library, 24. North-Holland Publishing Co., Amsterdam-New York; Kodansha, Ltd., Tokyo, 1981. xiv+464 pp. ISBN: 0-444-86172-6 MR0637061 (84b:60080)

  1. Imhof, J.-P. Density factorizations for Brownian motion, meander and the three-dimensional Bessel process, and applications. J. Appl. Probab. 21 (1984), no. 3, 500--510. MR0752015 (85j:60152)

  1. ItÙ, Kiyosi; McKean, Henry P., Jr. Diffusion processes and their sample paths. Second printing, corrected. Die Grundlehren der mathematischen Wissenschaften, Band 125. Springer-Verlag, Berlin-New York, 1974. xv+321 pp. MR0345224 (49 #9963)

  1. Jacod, Jean; MÈmin, Jean. Weak and strong solutions of stochastic differential equations: existence and stability. Stochastic integrals (Proc. Sympos., Univ. Durham, Durham, 1980), pp. 169--212, Lecture Notes in Math., 851, Springer, Berlin-New York, 1981. MR0620991 (83h:60062)

  1. Kunita, Hiroshi. Stochastic flows and stochastic differential equations. Cambridge Studies in Advanced Mathematics, 24. Cambridge University Press, Cambridge, 1990. xiv+346 pp. ISBN: 0-521-35050-6 MR1070361 (91m:60107)

  1. Lions, P.-L.; Sznitman, A.-S. Stochastic differential equations with reflecting boundary conditions. Comm. Pure Appl. Math. 37 (1984), no. 4, 511--537. MR0745330 (85m:60105)

  1. Pilipenko, A. Yu. Stochastic flows with reflection. Preprint, available on arXiv:0810.4644. Math. Review number not available.

  1. Pilipenko, A. Yu. Properties of flows generated by stochastic equations with reflection. (Russian) UkraÔn. Mat. Zh. 57 (2005), no. 8, 1069--1078; translation in Ukrainian Math. J. 57 (2005), no. 8, 1262--1274 MR2218469 (2007g:60066)

  1. Pilipenko, A. Yu. Stochastic flows with reflection. (Russian) Dopov. Nats. Akad. Nauk Ukr. Mat. Prirodozn. Tekh. Nauki 2005, no. 10, 23--28. MR2218498 (2007j:60089)

  1. Pilipenko, A. Yu. On the generalized differentiability with initial data of a flow generated by a stochastic equation with reflection. (Ukrainian) Teor. ?movīr. Mat. Stat. No. 75 (2006), 127--139; translation in Theory Probab. Math. Statist. No. 75 (2007), 147--160 MR2321188 (2008e:60179)

  1. Revuz, Daniel; Yor, Marc. Continuous martingales and Brownian motion. Third edition. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 293. Springer-Verlag, Berlin, 1999. xiv+602 pp. ISBN: 3-540-64325-7 MR1725357 (2000h:60050)

  1. Sheu, Shey Shiung. Noncoalescence of Brownian motion reflecting on a sphere. Stochastic Anal. Appl. 19 (2001), no. 4, 545--554. MR1841943 (2002f:60161)

  1. Tanaka, Hiroshi. Stochastic differential equations with reflecting boundary condition in convex regions. Hiroshima Math. J. 9 (1979), no. 1, 163--177. MR0529332 (80k:60075)

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.