Stochastic integration of operator-valued functions with respect to banach space-valued brownian motion

Potential Analysis

Volumn 29, Issue 1, 2008, Pages 65-88

  Van Neerven, J M A M ^a   Weis, L ^b  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

Radonifying operators; Measurable linear extensions; Property( ); Stochastic evolution equations; Stochastic integration in Banach spaces

Indexed keywords

EID: 47249086777     PISSN: 09262601     EISSN: 1572929X     Source Type: Journal    
DOI: 10.1007/s11118-008-9088-2     Document Type: Article

References (28)

1. Anderson, T.W.: The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities. Proc. Amer. Math. Soc. 6, 170-176 (1955)
2. Bogachev, V.I.: Gaussian Measures. Math. Surveys and Monographs, vol. 62. Amer. Math. Soc., Providence, RI (1998)
3. Brzeźniak, Z., van Neerven, J.M.A.M.: Stochastic convolution in separable Banach spaces and the stochastic linear Cauchy problem. Studia Math. 143, 43-74 (2000)
4. Clément, Ph., de Pagter, B., Sukochev, F., Witvliet, H.: Schauder decompositions and multiplier theorems. Studia Math. 138, 135-163 (2000)
5. Denk, R., Hieber, M., Prüss, J.: R-boundedness, Fourier multipliers and problems of elliptic and parabolic type. Mem. Amer. Math. Soc. 166, 788 (2003)
6. Diestel, J., Jarchow, H., Tonge, A.: Absolutely Summing Operators. Cambridge Studies in Adv. Math., vol. 34. Cambridge (1995)
7. p -spaces. J. Operator Theory 17, 255-279 (1987)
8. Feyel, D., de la Pradelle, A.: Opérateurs linéaires et gaussiens. Potential Anal. 3, 89-105 (1994)
9. Haak, B.: Kontrolltheorie in Banachräumen und Quadratische Abschätzungen. Ph.D. thesis, University of Karlsruhe (2004)
10. Itô, K., Nisio, M.: On the convergence of sums of independent Banach space valued random variables. Osaka J. Math. 5, 35-48 (1968)
11. ∞-functional calculus and square function estimates (in preparation)
12. ∞- functional calculus. In: Springer Lect. Notes Math. 1855, pp. 65-311. Springer-Verlag (2004)
13. Kwapień, S., Woyczyński, W.A.: Random Series and Stochastic Integrals: Single and Multiple, Probability and Its Applications. Birkhäuser Verlag, Boston (1992)
14. Ledoux, M., Talagrand, M.: Probability in Banach Spaces. Ergebnisse d. Math. u. ihre Grenzgebiete, vol. 23. Springer-Verlag (1991)
15. Le Merdy, C.: The Weiss conjecture for bounded analytic semigroups. J. London Math. Soc. 67, 715-738 (2003)
16. p ; (1∈<∈p∈<∈∞). C. R. Acad. Sci. Paris Sér. I Math. 303, 289-292 (1986)
17. Mamporia, B.I.: The stochastic integral of an operator-valued function with respect to a vector-valued Wiener process. Bull. Acad. Sci. Georgian SSR 105, 29-32 (1982)
18. van Neerven, J.M.A.M., Weis, L.: Stochastic integration of functions with values in a Banach space. Studia Math. 166, 131-170 (2005)
19. de Pagter, B., Ricker, W.: Products of commuting Boolean algebras of projections and Banach space geometry. Proc. London Math. Soc. 91, 483-508 (2005)
20. Pisier, G.: Some results on Banach spaces without local unconditional structure. Compositio Math. 37, 3-19 (1978)
21. Pisier, G.: Holomorphic semigroups and the geometry of Banach spaces. Ann. of Math. 115(2), 375-392 (1982)
22. Pisier, G.: The Volume of Convex Bodies and Banach Space Geometry. Cambridge Tracts in Mathematics, vol. 94. Cambridge (1989)
23. p -spaces. In: Handbook of the Geometry of Banach Spaces, vol. 2. Elsevier (2003)
24. Rosiński, J.: Bilinear random integrals. Dissertationes Mathematicae, vol. 259, 71 pp. (1987)
25. Rosiński, J., Suchanecki, Z.: On the space of vector-valued functions integrable with respect to the white noise. Colloq. Math. 43, 183-201 (1980)
26. p (1≤∈p∈< ∈∞∈). Studia Math. 50, 163-182 (1974)
27. Vakhania, N.N., Tarieladze, V.I., Chobanyan, S.A.: Probability Distributions in Banach Spaces. D. Reidel Publishing Company, Dordrecht (1987)
28. Zimmermann, F.: On vector-valued Fourier multiplier theorems. Studia Math. 93, 201-222 (1989)