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


  • Applebaum, David. Martingale-valued measures, Ornstein-Uhlenbeck processes with jumps and operator self-decomposability in Hilbert space. In memoriam Paul-André Meyer: Séminaire de Probabilités XXXIX, 171--196, Lecture Notes in Math., 1874, Springer, Berlin, 2006. MR2276896
  • Applebaum, David. Lévy processes and stochastic calculus. Second edition. Cambridge Studies in Advanced Mathematics, 116. Cambridge University Press, Cambridge, 2009. xxx+460 pp. ISBN: 978-0-521-73865-1 MR2512800
  • Applebaum, David. Universal Malliavin calculus in Fock and Lévy-Itô spaces. Commun. Stoch. Anal. 3 (2009), no. 1, 119--141. MR2541741
  • Applebaum, David. On the infinitesimal generators of Ornstein-Uhlenbeck processes with jumps in Hilbert space. Potential Anal. 26 (2007), no. 1, 79--100. MR2276526
  • Bogachev, Vladimir I. Gaussian measures. Mathematical Surveys and Monographs, 62. American Mathematical Society, Providence, RI, 1998. xii+433 pp. ISBN: 0-8218-1054-5 MR1642391
  • Bogachev, Vladimir I.; Röckner, Michael; Schmuland, Byron. Generalized Mehler semigroups and applications. Probab. Theory Related Fields 105 (1996), no. 2, 193--225. MR1392452
  • Chojnowska-Michalik, Anna. On processes of Ornstein-Uhlenbeck type in Hilbert space. Stochastics 21 (1987), no. 3, 251--286. MR0900115
  • Chojnowska-Michalik, Anna; Goldys, Beniamin. Nonsymmetric Ornstein-Uhlenbeck semigroup as second quantized operator. J. Math. Kyoto Univ. 36 (1996), no. 3, 481--498. MR1417822
  • Chojnowska-Michalik, Anna; Goldys, Beniamin. Symmetric Ornstein-Uhlenbeck semigroups and their generators. Probab. Theory Related Fields 124 (2002), no. 4, 459--486. MR1942319
  • Dawson, D. A.; Li, Zenghu. Skew convolution semigroups and affine Markov processes. Ann. Probab. 34 (2006), no. 3, 1103--1142. MR2243880
  • Dawson, Donald A.; Li, Zenghu; Schmuland, Byron; Sun, Wei. Generalized Mehler semigroups and catalytic branching processes with immigration. Potential Anal. 21 (2004), no. 1, 75--97. MR2048508
  • Eddahbi, M.; Solé, J. L.; Vives, J. A Stroock formula for a certain class of Lévy processes and applications to finance. J. Appl. Math. Stoch. Anal. 2005, no. 3, 211--235. MR2203030
  • Feyel, Denis; de La Pradelle, Arnaud. Opérateurs linéaires gaussiens. (French) [Gaussian linear operators] Proceedings from the International Conference on Potential Theory (Amersfoort, 1991). Potential Anal. 3 (1994), no. 1, 89--105. MR1266219
  • Fuhrman, Marco; Röckner, Michael. Generalized Mehler semigroups: the non-Gaussian case. Potential Anal. 12 (2000), no. 1, 1--47. MR1745332
  • Goldys, B.; van Neerven, J. M. A. M. Transition semigroups of Banach space-valued Ornstein-Uhlenbeck processes. Acta Appl. Math. 76 (2003), no. 3, 283--330. MR1976297
  • Guichardet, Alain. Symmetric Hilbert spaces and related topics. Infinitely divisible positive definite functions. Continuous products and tensor products. Gaussian and Poissonian stochastic processes. Lecture Notes in Mathematics, Vol. 261. Springer-Verlag, Berlin-New York, 1972. v+197 pp. MR0493402
  • Heyer, Herbert. Structural aspects in the theory of probability. A primer in probabilities on algebraic-topological structures. Series on Multivariate Analysis, 7. World Scientific Publishing Co., Inc., River Edge, NJ, 2004. x+388 pp. ISBN: 981-238-937-7 MR2111057
  • Jurek, Zbigniew J. An integral representation of operator-self-decomposable random variables. Bull. Acad. Polon. Sci. Sér. Sci. Math. 30 (1982), no. 7-8, 385--393. MR0707753
  • Jurek, Zbigniew J.; Vervaat, Wim. An integral representation for self-decomposable Banach space valued random variables. Z. Wahrsch. Verw. Gebiete 62 (1983), no. 2, 247--262. MR0688989
  • Last, Günter; Penrose, Mathew D. Poisson process Fock space representation, chaos expansion and covariance inequalities. Probab. Theory Related Fields 150 (2011), no. 3-4, 663--690. MR2824870
  • Linde, Werner. Probability in Banach spaces—stable and infinitely divisible distributions. Second edition. A Wiley-Interscience Publication. John Wiley & Sons, Ltd., Chichester, 1986. 195 pp. ISBN: 0-471-90893-2 MR0874529
  • Maas, Jan; van Neerven, Jan. Boundedness of Riesz transforms for elliptic operators on abstract Wiener spaces. J. Funct. Anal. 257 (2009), no. 8, 2410--2475. MR2555015
  • van Neerven, J. M. A. M. Nonsymmetric Ornstein-Uhlenbeck semigroups in Banach spaces. J. Funct. Anal. 155 (1998), no. 2, 495--535. MR1624573
  • van Neerven, J. M. A. M. Second quantization and the $L^ p$-spectrum of nonsymmetric Ornstein-Uhlenbeck operators. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 8 (2005), no. 3, 473--495. MR2172310
  • van Neerven, J. M. A. M.; Weis, L. Stochastic integration of functions with values in a Banach space. Studia Math. 166 (2005), no. 2, 131--170. MR2109586
  • Nualart, David. Malliavin calculus and its applications. CBMS Regional Conference Series in Mathematics, 110. Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 2009. viii+85 pp. ISBN: 978-0-8218-4779-4 MR2498953
  • Parthasarathy, K. R. An introduction to quantum stochastic calculus. [2012 reprint of the 1992 original] [ MR1164866 (93g:81062)]. Modern Birkhäuser Classics. Birkhäuser/Springer Basel AG, Basel, 1992. xii+290 pp. ISBN: 978-3-0348-0565-0; 978-3-0348-0566-7 MR3012668
  • Peszat, S. Lévy-Ornstein-Uhlenbeck transition semigroup as second quantized operator. J. Funct. Anal. 260 (2011), no. 12, 3457--3473. MR2781967
  • Peszat, S.; Zabczyk, J. Stochastic partial differential equations with Lévy noise. An evolution equation approach. Encyclopedia of Mathematics and its Applications, 113. Cambridge University Press, Cambridge, 2007. xii+419 pp. ISBN: 978-0-521-87989-7 MR2356959
  • Riedle, Markus; van Gaans, Onno. Stochastic integration for Lévy processes with values in Banach spaces. Stochastic Process. Appl. 119 (2009), no. 6, 1952--1974. MR2519352
  • Röckner, Michael; Wang, Feng-Yu. Harnack and functional inequalities for generalized Mehler semigroups. J. Funct. Anal. 203 (2003), no. 1, 237--261. MR1996872
  • Stroock, Daniel W. Homogeneous chaos revisited. Séminaire de Probabilités, XXI, 1--7, Lecture Notes in Math., 1247, Springer, Berlin, 1987. MR0941972
  • Urbanik, K. Lévy's probability measures on Banach spaces. Studia Math. 63 (1978), no. 3, 283--308. MR0515497
  • Vakhania, N. N.; Tarieladze, V. I.; Chobanyan, S. A. Probability distributions on Banach spaces. Translated from the Russian and with a preface by Wojbor A. Woyczynski. Mathematics and its Applications (Soviet Series), 14. D. Reidel Publishing Co., Dordrecht, 1987. xxvi+482 pp. ISBN: 90-277-2496-2 MR1435288

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