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


  • Barlow, M. T. Skew Brownian motion and a one-dimensional stochastic differential equation. Stochastics 25 (1988), no. 1, 1--2. MR1008231
  • Barlow, M. T. One-dimensional stochastic differential equations with no strong solution. J. London Math. Soc. (2) 26 (1982), no. 2, 335--347. MR0675177
  • Bass, Richard. Markov processes with Lipschitz semigroups. Trans. Amer. Math. Soc. 267 (1981), no. 1, 307--320. MR0621990
  • Bass, Richard F. Probabilistic techniques in analysis. Probability and its Applications (New York). Springer-Verlag, New York, 1995. xii+392 pp. ISBN: 0-387-94387-0 MR1329542
  • Bass, Richard F. Diffusions and elliptic operators. Probability and its Applications (New York). Springer-Verlag, New York, 1998. xiv+232 pp. ISBN: 0-387-98315-5 MR1483890
  • Bass, Richard F. Stochastic processes. Cambridge Series in Statistical and Probabilistic Mathematics, 33. Cambridge University Press, Cambridge, 2011. xvi+390 pp. ISBN: 978-1-107-00800-7 MR2856623
  • Bass, Richard F.; Burdzy, Krzysztof; Chen, Zhen-Qing. Pathwise uniqueness for a degenerate stochastic differential equation. Ann. Probab. 35 (2007), no. 6, 2385--2418. MR2353392
  • Chernyĭ, A. S. On strong and weak uniqueness for stochastic differential equations. (Russian) Teor. Veroyatnost. i Primenen. 46 (2001), no. 3, 483--497; translation in Theory Probab. Appl. 46 (2003), no. 3, 406--419 MR1978664
  • Chitashvili, R. On the nonexistence of a strong solution in the boundary problem for a sticky Brownian motion. Proc. A. Razmadze Math. Inst. 115 (1997), 17--31. MR1639096
  • Engelbert, H. J. On the theorem of T. Yamada and S. Watanabe. Stochastics Stochastics Rep. 36 (1991), no. 3-4, 205--216. MR1128494
  • H.J. Engelbert and G. Peskir, Stochastic differential equations for sticky Brownian motions. Probab. Statist. Group Manchester Research Report (5).
  • Engelbert, H. J.; Schmidt, W. Strong Markov continuous local martingales and solutions of one-dimensional stochastic differential equations. III. Math. Nachr. 151 (1991), 149--197. MR1121203
  • Itô, 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
  • Karatzas, Ioannis; Shreve, Steven E. Brownian motion and stochastic calculus. Second edition. Graduate Texts in Mathematics, 113. Springer-Verlag, New York, 1991. xxiv+470 pp. ISBN: 0-387-97655-8 MR1121940
  • Karatzas, Ioannis; Shiryaev, Albert N.; Shkolnikov, Mykhaylo. On the one-sided Tanaka equation with drift. Electron. Commun. Probab. 16 (2011), 664--677. MR2853104
  • Knight, Frank B. Essentials of Brownian motion and diffusion. Mathematical Surveys, 18. American Mathematical Society, Providence, R.I., 1981. xiii+201 pp. ISBN: 0-8218-1518-0 MR0613983
  • Knight, Frank B. A reduction of continuous square-integrable martingales to Brownian motion. Martingales (Rep. Meeting, Oberwolfach, 1970), pp. 19--31. Lecture Notes in Math., Vol. 190, Springer, Berlin, 1971. MR0370741
  • Kurtz, Thomas G. The Yamada-Watanabe-Engelbert theorem for general stochastic equations and inequalities. Electron. J. Probab. 12 (2007), 951--965. MR2336594
  • Kurtz, Thomas G.; Protter, Philip. Weak limit theorems for stochastic integrals and stochastic differential equations. Ann. Probab. 19 (1991), no. 3, 1035--1070. MR1112406
  • Le Gall, J.-F. Applications du temps local aux équations différentielles stochastiques unidimensionnelles. (French) [Local time applications to one-dimensional stochastic differential equations] Seminar on probability, XVII, 15--31, Lecture Notes in Math., 986, Springer, Berlin, 1983. MR0770393
  • Nakao, Shintaro. On the pathwise uniqueness of solutions of one-dimensional stochastic differential equations. Osaka J. Math. 9 (1972), 513--518. MR0326840
  • 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
  • Warren, Jonathan. Branching processes, the Ray-Knight theorem, and sticky Brownian motion. Séminaire de Probabilités, XXXI, 1--15, Lecture Notes in Math., 1655, Springer, Berlin, 1997. MR1478711
  • Warren, J. On the joining of sticky Brownian motion. Séminaire de Probabilités, XXXIII, 257--266, Lecture Notes in Math., 1709, Springer, Berlin, 1999. MR1767999

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