Download this PDF file Fullscreen Fullscreen Off
References
- Albeverio, S.; Kondratiev, Yu. G.; Röckner, M. Uniqueness of the stochastic dynamics for continuous spin systems on a lattice. J. Funct. Anal. 133 (1995), no. 1, 10--20. MR1351639 (96i:31006)
- Albeverio, S.; Kondratiev, Yu. G.; Tsikalenko, T. V. Stochastic dynamics for quantum lattice systems and stochastic quantization. I. Ergodicity.Translated by the authors. Random Oper. Stochastic Equations 2 (1994), no. 2, 103--139. MR1293068 (95i:82008)
- Albeverio, S.; Mandrekar, V.; Rüdiger, B. Existence of mild solutions for stochastic differential equations and semilinear equations with non-Gaussian Lévy noise. Stochastic Process. Appl. 119 (2009), no. 3, 835--863. MR2499860 (2010e:60113)
- Albeverio, Sergio; Rüdiger, Barbara; Wu, Jiang-Lun. Invariant measures and symmetry property of Lévy type operators. Potential Anal. 13 (2000), no. 2, 147--168. MR1782254 (2001i:60138)
- Albeverio, Sergio; Wu, Jiang-Lun; Zhang, Tu-Sheng. Parabolic SPDEs driven by Poisson white noise. Stochastic Process. Appl. 74 (1998), no. 1, 21--36. MR1624076 (99c:60124)
- Bakry, Dominique; Émery, Michel. Inégalités de Sobolev pour un semi-groupe symétrique.(French) [Sobolev inequalities for a symmetric semigroup] C. R. Acad. Sci. Paris Sér. I Math. 301 (1985), no. 8, 411--413. MR0808640 (86k:60141)
- Bass, Richard F.; Chen, Zhen-Qing. Systems of equations driven by stable processes. Probab. Theory Related Fields 134 (2006), no. 2, 175--214. MR2222382 (2007k:60164)
- Bertoin, Jean. Lévy processes.Cambridge Tracts in Mathematics, 121. Cambridge University Press, Cambridge, 1996. x+265 pp. ISBN: 0-521-56243-0 MR1406564 (98e:60117)
- Bichteler, Klaus. Stochastic integration with jumps.Encyclopedia of Mathematics and its Applications, 89. Cambridge University Press, Cambridge, 2002. xiv+501 pp. ISBN: 0-521-81129-5 MR1906715 (2003d:60002)
- Spin glasses.Edited by Erwin Bolthausen and Anton Bovier.Lecture Notes in Mathematics, 1900. Springer, Berlin, 2007. x+179 pp. ISBN: 978-3-540-40902-1; 3-540-40902-5 MR2309595 (2007k:82149)
- 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 (95g:60073)
- Giuseppe Da Prato and Jerzy Zabczyk, Ergodicity for infinite-dimensional systems, London Mathematical Society Lecture Note Series, vol. 229, Cambridge University Press, Cambridge, 1996.
- Don Dawson, Stochastic population dynamics, (2009),http://www.math.ubc.ca/~db5d/SummerSchool09/lectures-dd/lecture14.pdf
- Folland, Gerald B. Real analysis.Modern techniques and their applications.Second edition.Pure and Applied Mathematics (New York). A Wiley-Interscience Publication.John Wiley & Sons, Inc., New York, 1999. xvi+386 pp. ISBN: 0-471-31716-0 MR1681462 (2000c:00001)
- Funaki, Tadahisa; Xie, Bin. A stochastic heat equation with the distributions of Lévy processes as its invariant measures. Stochastic Process. Appl. 119 (2009), no. 2, 307--326. MR2493992 (2010g:60153)
- Greven, A.; den Hollander, F. Phase transitions for the long-time behavior of interacting diffusions. Ann. Probab. 35 (2007), no. 4, 1250--1306. MR2330971 (2008h:60405)
- Guionnet, A.; Zegarlinski, B. Lectures on logarithmic Sobolev inequalities. Séminaire de Probabilités, XXXVI, 1--134, Lecture Notes in Math., 1801, Springer, Berlin, 2003. MR1971582 (2004b:60226)
- Hairer, Martin; Mattingly, Jonathan C. Ergodicity of the 2D Navier-Stokes equations with degenerate stochastic forcing. Ann. of Math. (2) 164 (2006), no. 3, 993--1032. MR2259251 (2008a:37095)
- M. Hutzenthaler and A. Wakolbinger, Ergodic behavior of locally regulated branching populations, Ann. Appl. Probab. 17 (2007), no. 2, 474--501.
- 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)
- Carlo Marinelli and Michael R?ckner, Well-posedness and asymptotic behavior for stochastic reaction-diffusion equations with multiplicative poisson noise, arXiv:0903.3299v2.
- Øksendal, Bernt. Stochastic partial differential equations driven by multi-parameter white noise of Lévy processes. Quart. Appl. Math. 66 (2008), no. 3, 521--537. MR2445527 (2009i:60128)
- Robert Olkiewicz, Lihu Xu, and Boguslaw Zegarlinski, Nonlinear problems in infinite interacting particle systems, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 11 (2008), no. 2, 179--211.
- 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 (2009b:60200)
- Peszat, Szymon; Zabczyk, Jerzy. Stochastic heat and wave equations driven by an impulsive noise. Stochastic partial differential equations and applications—VII, 229--242, Lect. Notes Pure Appl. Math., 245, Chapman & Hall/CRC, Boca Raton, FL, 2006. MR2227232 (2007h:60056)
- Pistorius, Martijn R. An excursion-theoretical approach to some boundary crossing problems and the Skorokhod embedding for reflected Lévy processes. Séminaire de Probabilités XL, 287--307, Lecture Notes in Math., 1899, Springer, Berlin, 2007. MR2409012 (2009e:60105)
- E. Priola and J. Zabczyk, Structural properties of semilinear spdes driven by cylindrical stable processes, Probab. Theory Related Fields (2009), (to appear).
- Priola, Enrico; Zabczyk, Jerzy. Densities for Ornstein-Uhlenbeck processes with jumps. Bull. Lond. Math. Soc. 41 (2009), no. 1, 41--50. MR2481987 (2010f:60241)
- Rogers, L. C. G.; Williams, David. Diffusions, Markov processes, and martingales. Vol. 1.Foundations.Reprint of the second (1994) edition.Cambridge Mathematical Library. Cambridge University Press, Cambridge, 2000. xx+386 pp. ISBN: 0-521-77594-9 MR1796539 (2001g:60188)
- Marco Romito and Lihu Xu, Ergodicity of the 3d stochastic navier-stokes equations driven by mildly degenerate noise, 2009, preprint.
- Rost, Hermann. Skorokhod's theorem for general Markov processes. Transactions of the Sixth Prague Conference on Information Theory, Statistical Decision Functions, Random Processes (Tech. Univ. Prague, Prague, 1971; dedicated to the memory of Antonín Špaček), pp. 755--764. Academia, Prague, 1973. MR0356248 (50 #8719)
- Lihu Xu, Stochastic population dynamics, Lecture notes based on the lectures given by Don Dawson at summer school of UBC in 2009 (pp 44, still being writing in progress).
- Lihu Xu and Boguslaw Zegarlinski, Ergodicity of the finite and infinite dimensional $\alpha$-stable systems, Stoch. Anal. Appl. 27 (2009), no.~4, 797--824.
- Xu, Lihu; Zegarliński, Bogusław. Ergodicity of the finite and infinite dimensional $\alpha$-stable systems. Stoch. Anal. Appl. 27 (2009), no. 4, 797--824. MR2541378 (2010k:60180)
- Boguslaw Zegarlinski, The strong decay to equilibrium for the stochastic dynamics of unbounded spin systems on a lattice, Comm. Math. Phys. 175 (1996), no.~2, 401--432.

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