Malliavin calculus and decoupling inequalities in Banach spaces

Journal of Mathematical Analysis and Applications

Volumn 363, Issue 2, 2010, Pages 383-398

  Maas, Jan ^a  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Decoupling inequalities; Gaussian chaos; Malliavin calculus; Meyer's inequalities; Meyer's multiplier theorem; Multiple stochastic integrals; Wiener It decomposition

Indexed keywords

EID: 70449088951     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2009.08.041     Document Type: Article

References (33)

1. Arcones M.A., and Giné E. On decoupling, series expansions, and tail behavior of chaos processes. J. Theoret. Probab. 6 1 (1993) 101-122
2. Arendt W., Batty C.J.K., Hieber M., and Neubrander F. Vector-Valued Laplace Transforms and Cauchy Problems. Monogr. Math. vol. 96 (2001), Birkhäuser Verlag, Basel
3. Bakhtin Y., and Mattingly J.C. Malliavin calculus for infinite-dimensional systems with additive noise. J. Funct. Anal. 249 2 (2007) 307-353
4. Bogachev V.I. Gaussian Measures. Math. Surveys Monogr. vol. 62 (1998), American Mathematical Society, Providence, RI
5. Burkholder D.L. Martingales and singular integrals in Banach spaces. Handbook of the Geometry of Banach Spaces, vol. I (2001), North-Holland, Amsterdam 233-269
6. Carmona R.A., and Tehranchi M.R. Interest Rate Models: An Infinite Dimensional Stochastic Analysis Perspective. Springer Finance (2006), Springer-Verlag, Berlin
7. de la Peña V.H., and Giné E. Decoupling. Probab. Appl. (N. Y.) (1999), Springer-Verlag, New York
8. de la Peña V.H., and Montgomery-Smith S.J. Decoupling inequalities for the tail probabilities of multivariate U-statistics. Ann. Probab. 23 2 (1995) 806-816
9. Figiel T., and Tomczak-Jaegermann N. Projections onto Hilbertian subspaces of Banach spaces. Israel J. Math. 33 2 (1979) 155-171
10. Hairer M., Mattingly J.C., and Pardoux E. Malliavin calculus for highly degenerate 2D stochastic Navier-Stokes equations. C. R. Math. Acad. Sci. Paris 339 11 (2004) 793-796
11. Hytönen T.P. Littlewood-Paley-Stein theory for semigroups in UMD spaces. Rev. Mat. Iberoamericana 23 3 (2007) 973-1009
12. Ikeda N., and Watanabe S. Stochastic Differential Equations and Diffusion Processes. North-Holland Math. Library. second ed. vol. 24 (1989), North-Holland Publishing Co., Amsterdam
13. ∞-functional calculus and square function estimates, in preparation
14. Kwapień S. Decoupling inequalities for polynomial chaos. Ann. Probab. 15 3 (1987) 1062-1071
15. Kwapień S., and Woyczyński W.A. Random Series and Stochastic Integrals: Single and Multiple. Probab. Appl. (1992), Birkhäuser Boston Inc., Boston, MA
16. Maas J., and van Neerven J.M.A.M. A Clark-Ocone formula in UMD Banach spaces. Electron. Comm. Probab. 13 (2008) 151-164
17. Malliavin P. Stochastic calculus of variation and hypoelliptic operators. Proceedings of the International Symposium on Stochastic Differential Equations, Res. Inst. Math. Sci., Kyoto Univ. Kyoto, 1976 (1978), Wiley, New York 195-263
18. Malliavin P., and Nualart D. Quasi-sure analysis and Stratonovich anticipative stochastic differential equations. Probab. Theory Related Fields 96 1 (1993) 45-55
19. Mayer-Wolf E., and Zakai M. The divergence of Banach space valued random variables on Wiener space. Probab. Theory Related Fields 132 2 (2005) 291-320
20. Mayer-Wolf E., and Zakai M. Erratum: "The divergence of Banach space valued random variables on Wiener space" [Probab. Theory Related Fields 132 (2) (2005) 291-320, MR2199294]. Probab. Theory Related Fields 140 3-4 (2008) 631-633
21. McConnell T.R., and Taqqu M.S. Decoupling inequalities for multilinear forms in independent symmetric random variables. Ann. Probab. 14 3 (1986) 943-954
22. McConnell T.R., and Taqqu M.S. Decoupling of Banach-valued multilinear forms in independent symmetric Banach-valued random variables. Probab. Theory Related Fields 75 4 (1987) 499-507
23. Meyer P.-A. Transformations de Riesz pour les lois gaussiennes. Seminar on Probability, XVIII. Lecture Notes in Math. vol. 1059 (1984), Springer, Berlin 179-193
24. van Neerven J.M.A.M., Veraar M.C., and Weis L. Stochastic integration in UMD Banach spaces. Ann. Probab. 35 4 (2007) 1438-1478
25. van Neerven J.M.A.M., Veraar M.C., and Weis L. Stochastic evolution equations in UMD Banach spaces. J. Funct. Anal. 255 4 (2008) 940-993
26. van Neerven J.M.A.M., and Weis L. Stochastic integration of functions with values in a Banach space. Studia Math. 166 2 (2005) 131-170
27. van Neerven J.M.A.M., and Weis L. Stochastic integration of operator-valued functions with respect to Banach space-valued Brownian motion. Potential Anal. 29 1 (2008) 65-88
28. Nualart D. The Malliavin Calculus and Related Topics. Probab. Appl. (N. Y.). second ed. (2006), Springer-Verlag, Berlin
29. Pisier G. Some results on Banach spaces without local unconditional structure. Compos. Math. 37 1 (1978) 3-19
30. Pisier G. Holomorphic semigroups and the geometry of Banach spaces. Ann. of Math. (2) 115 2 (1982) 375-392
31. Pisier G. Riesz transforms: A simpler analytic proof of P.-A. Meyer's inequality. Séminaire de Probabilités, XXII. Lecture Notes in Math. vol. 1321 (1988), Springer, Berlin 485-501
32. Pisier G. The Volume of Convex Bodies and Banach Space Geometry. Cambridge Tracts in Math. vol. 94 (1989), Cambridge University Press, Cambridge
33. Shigekawa I. Sobolev spaces of Banach-valued functions associated with a Markov process. Probab. Theory Related Fields 99 3 (1994) 425-441