Generalized Mehler Semigroups: The Non-Gaussian Case

Potential Analysis

Volumn 12, Issue 1, 2000, Pages 1-47

  Fuhrman, Marco ^a   Röckner, Michael ^b  

^a POLITECNICO DI MILANO   (Italy)

^b BIELEFELD UNIVERSITY   (Germany)

Author keywords

Cadlag processes in abstract spaces; Markovian semigroups; Mehler formula; Tightness of capacities

Indexed keywords

EID: 0042640592     PISSN: 09262601     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008644017078     Document Type: Article

References (40)

1. Albeverio, S. and Röckner, M.: 'Classical Dirichlet forms on topological vector spaces - the construction of the associated diffusion process', Probab. Th. Rel. Fields 83 (1989), 405-434.
2. Albeverio, S., Fukushima, M., Hansen, W., Ma, Z. M. and Röckner, M.: 'An invariance result for capacities on Wiener space', J. Functional Anal. 106 (1992), 35-49.
3. Bauer, H.: Wahrscheinlichkeitstheorie und Grundzüge der Maβtheorie, de Gruyter, 1978.
4. Berg, C. and Forst, G.: Potential Theory on Locally Compact Abelian Groups, Springer, 1975.
5. Bogachev, V. I. and Röckner, M.: 'Mehler formula and capacities for infinite-dimensional Ornstein-Uhlenbeck processes with general linear drift', Osaka J. Math. 32 (1995), 237-274.
6. Bogachev, V. I., Lescot, P. and Röckner, M.: The Martingale Problem for Pseudo-differential Operators on Infinite-dimensional Spaces, preprint '95-093 SFB 343, Universität Bielefeld. (1995).
7. Bogachev, V. I., Röckner, M. and Schmuland, B.: 'Generalized Mehler semigroups and applications', Probab. Theory Relat. Fields 105 (1996), 193-225.
8. Bouleau, N. and Hirsch, F.: 'Some results on Lipschitzian stochastic differential equations by Dirichlet forms methods', in: Stochastic Analysis and Related Topics, II (Silivri, 1988), 128-140, LNM 1444, Springer, 1990.
9. Bouleau, N. and Hirsch, F.: 'Quasi-everywhere regularity of solutions of Brownian stochastic differential equations and their flows', J. Math. Pures Appl. (9) 69 (1) (1990), 95-128.
10. Cerrai, S.: 'A Hille-Yosida theorem for weakly continuous semigroups', Semigroup Forum 49 (1994), 349-367.
11. Cerrai, S. and Gozzi, F.: Strong Solutions of Cauchy Problems Associated to Weakly Continuous Semigroups, preprint no. 35, Scuola Normale Superiore Pisa, December 1993.
12. Chojnowska-Michalik, A.: 'On processes of Ornstein-Uhlenbeck type in Hilbert space', Stochastics Stochastics Rep. 21 (1987), 251-286.
13. Da Prato, G. and Zabczyk, J.: Stochastic Equations in Infinite Dimensions, Encyclopedia of mathematics and its applications 44, Cambridge University Press, 1992.
14. Davies, E.B.: One-parameter Semigroups, Academic Press, 1980.
15. Feyel, D. and de La Pradelle, A.: 'Espaces de Sobolev gaussiens', Ann. Inst. Fourier 39(4) (1989), 875-908.
16. Feyel, D. and de La Pradelle, A.: 'Sur les capacités gaussiennes en dimension infinie', C.R. Acad. Sci. Paris 308, Série I (1989), 489-491.
17. Feyel, D. and de La Pradelle, A.: 'Operateurs lineaires et espaces de Sobolev sur l'espace de Wiener', C.R. Acad. Sci. Paris 313, Série I (1991), 727-729.
18. Feyel, D. and de La Pradelle, A.: 'Capacités gaussiennes', Ann. Inst. Fourier 41(1) (1991), 49-76.
19. Feyel, D. and de La Pradelle, A.: 'Operateurs lineaires gaussiens', Potential Analysis 3 (1994), 89-105.
20. Feyel, D. and de La Pradelle, A.: 'On infinite-dimensional sheets', Potential Analysis 4 (1995), 345-359.
21. Feyel, D. and de La Pradelle, A.: 'Brownian processes in infinite dimension', Potential Analysis, 4 (1995), 173-183.
22. Fukushima, M. and Kaneko, H.: (r, p)-capacities for general Markovian semigroups, in: Proc. USP-meeting Bielefeld, Stochastic processes and infinite dimensional analysis, S. Albeverio (ed.), Pitman, 1983, pp. 41-47.
23. Gross, L.: 'Abstract Wiener Spaces', in: Proc. 5th Berkeley Symp. Math. Stat. Prob. 1965, 2 (1965), 31-42.
24. Hirsch, F.: 'Potential theory related to some multiparameter processes', Potential Analysis, 4 (1995), 245-267.
25. Hirsch, F. and Song, S.: 'Markov properties of multiparameter processes and capacities', Probab. Th. Rel. Fields 103 (1995), 45-71.
26. Kaneko, H.: 'On (r, p)-capacities for Markov processes', Osaka J. Math. 23 (1986), 325-336.
27. Kuo, H. H.: Gaussian Measures in Banach Spaces, Lecture Notes Math. 463, Springer, 1975.
28. Kusuoka, S.: 'Dirichlet forms and diffusion processes on Banach spaces', J. Fac. Science Univ. Tokyo, Sec. 1A 29 (1982), 79-95.
29. Linde, W.: Probability in Banach Spaces - Stable and Infinitely Divisible Distributions, John Wiley and Sons, 1986.
30. Lyons, T. and Röckner, M.: 'A note on tightness of capacities associated with Dirichlet forms', Bull. London Math. Soc. 24 (1992), 181-184.
31. Parthasarathy, K. R.: Probability Measures on Metric Spaces, Academic Press, New York and London, 1967.
32. Pazy, A.: Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, 1983.
33. 1,p-capacities on Banach space', J. Funct. Anal. 108 (1992), 1-12.
34. Schmuland, B.: 'An alternative compactification for classical Dirichlet forms on topological vector spaces', Stochastics 33 (1990), 75-90.
35. 2,2-polaires', Potential Analysis 2 (1993), 171-186.
36. n,2, in: Séminaires de probabilités XXVII, LNM 1557, Springer, 1993.
37. Sugita, H.: 'Positive generalized Wiener functions and potential theory over abstract Wiener spaces', Osaka J. Math. 25 (1988), 665-696.
38. Vakhania, N. N., Tarieladze, V. I. and Chobanyan, S. A.: Probability Distributions on Banach Spaces, Reidel, 1987.
39. Wentzell, A. D.: A Course in the Theory of Stochastic Processes, McGraw-Hill, 1981.
40. Weron, A.: 'Stable processes and measures: A survey', in: Probability Theory on Vector Spaces III. Springer LNM 1080 (1984), 306-364.