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


  • Athreya, Siva R.; Bass, Richard F.; Gordina, Maria; Perkins, Edwin A. Infinite dimensional stochastic differential equations of Ornstein-Uhlenbeck type. Stochastic Process. Appl. 116 (2006), no. 3, 381--406. MR2199555
  • Bass, R. F. Uniqueness in law for pure jump Markov processes. Probab. Theory Related Fields 79 (1988), no. 2, 271--287. MR0958291
  • 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.; Perkins, Edwin A. Countable systems of degenerate stochastic differential equations with applications to super-Markov chains. Electron. J. Probab. 9 (2004), no. 22, 634--673 (electronic). MR2110015
  • R.F. Bass and E.A. Perkins, A new technique for proving uniqueness for martingale problems, In: From Probability to Geometry (I): Volume in Honor of the 60th Birthday of Jean-Michel Bismut, 47-53. Société Mathématique de France, Paris, 2009. MR2642351
  • Cannarsa, Piermarco; Da Prato, Giuseppe. Infinite-dimensional elliptic equations with Hölder-continuous coefficients. Adv. Differential Equations 1 (1996), no. 3, 425--452. MR1401401
  • Da Prato, Giuseppe; Zabczyk, Jerzy. Stochastic equations in infinite dimensions. Encyclopedia of Mathematics and its Applications, 44. Cambridge University Press, Cambridge, 1992. xviii+454 pp. ISBN: 0-521-38529-6 MR1207136
  • Horn, Roger A.; Johnson, Charles R. Matrix analysis. Cambridge University Press, Cambridge, 1985. xiii+561 pp. ISBN: 0-521-30586-1 MR0832183
  • Jaffard, S. Propriétés des matrices "bien localisées'' près de leur diagonale et quelques applications. (French) [Properties of matrices "well localized'' near their diagonal and some applications] Ann. Inst. H. Poincaré Anal. Non Linéaire 7 (1990), no. 5, 461--476. MR1138533
  • Kallianpur, Gopinath; Xiong, Jie. Stochastic differential equations in infinite-dimensional spaces. Expanded version of the lectures delivered as part of the 1993 Barrett Lectures at the University of Tennessee, Knoxville, TN, March 25–27, 1993. With a foreword by Balram S. Rajput and Jan Rosinski. Institute of Mathematical Statistics Lecture Notes—Monograph Series, 26. Institute of Mathematical Statistics, Hayward, CA, 1995. vi+342 pp. ISBN: 0-940600-38-2 MR1465436
  • Lax, Peter D. Functional analysis. Pure and Applied Mathematics (New York). Wiley-Interscience [John Wiley & Sons], New York, 2002. xx+580 pp. ISBN: 0-471-55604-1 MR1892228
  • Menozzi, Stéphane. Parametrix techniques and martingale problems for some degenerate Kolmogorov equations. Electron. Commun. Probab. 16 (2011), 234--250. MR2802040
  • C. Mueller, L. Mytnik, and E. Perkins, Nonuniqueness for a parabolic SPDE with 3/4-epsilon-Hölder diffusion coefficients, Preprint.
  • Mytnik, Leonid; Perkins, Edwin. Pathwise uniqueness for stochastic heat equations with Hölder continuous coefficients: the white noise case. Probab. Theory Related Fields 149 (2011), no. 1-2, 1--96. MR2773025
  • Revuz, Daniel; Yor, Marc. Continuous martingales and Brownian motion. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 293. Springer-Verlag, Berlin, 1991. x+533 pp. ISBN: 3-540-52167-4 MR1083357
  • Rogers, L. C. G.; Williams, David. Diffusions, Markov processes, and martingales. Vol. 2. Itô calculus. Reprint of the second (1994) edition. Cambridge Mathematical Library. Cambridge University Press, Cambridge, 2000. xiv+480 pp. ISBN: 0-521-77593-0 MR1780932
  • Stroock, Daniel W.; Varadhan, S. R. Srinivasa. Multidimensional diffusion processes. Reprint of the 1997 edition. Classics in Mathematics. Springer-Verlag, Berlin, 2006. xii+338 pp. ISBN: 978-3-540-28998-2; 3-540-28998-4 MR2190038
  • Walsh, John B. An introduction to stochastic partial differential equations. École d'été de probabilités de Saint-Flour, XIV—1984, 265--439, Lecture Notes in Math., 1180, Springer, Berlin, 1986. MR0876085
  • Yamada, Toshio; Watanabe, Shinzo. On the uniqueness of solutions of stochastic differential equations. J. Math. Kyoto Univ. 11 1971 155--167. MR0278420
  • Zambotti, Lorenzo. An analytic approach to existence and uniqueness for martingale problems in infinite dimensions. Probab. Theory Related Fields 118 (2000), no. 2, 147--168. MR1790079
  • Zygmund, A. Trigonometric series. Vol. I, II. Third edition. With a foreword by Robert A. Fefferman. Cambridge Mathematical Library. Cambridge University Press, Cambridge, 2002. xii; Vol. I: xiv+383 pp.; Vol. II: viii+364 pp. ISBN: 0-521-89053-5 MR1963498

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