Two results on continuity and boundedness of stochastic convolutions

Annales de l'institut Henri Poincare (B) Probability and Statistics

Volumn 42, Issue 5, 2006, Pages 553-566

  Kwapień, Stanisław ^a   Marcus, Michael B ^b   Rosiński, Jan ^c  

^a UNIVERSITY OF WARSAW   (Poland)

^b CITY COLLEGE OF NEW YORK   (United States)

^c UNIVERSITY OF TENNESSEE   (United States)

Author keywords

L vy processes; Sample boundedness; Sample continuity; Semimartingales; Stochastic convolution

Indexed keywords

EID: 33748689912     PISSN: 02460203     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.anihpb.2005.06.003     Document Type: Article

References (20)

1. Brzeźniak Z., Peszat S., and Zabczyk J. Continuity of stochastic convolutions. Czechoslovak Math. J. 51 (2001) 679-684
2. Da Prato G., and Zabczyk J. Stochastic Equations in Infinite Dimensions. Encyclopedia Math. Appl. vol. 45 (1992), Cambridge Univ. Press, Cambridge
3. de Acosta A. Exponential moments of vector valued random series and triangular arrays. Ann. Probab. 8 (1980) 381-389
4. Dinculeanu N. Vector Integration and Stochastic Integration in Banach Spaces (2000), Willey & Sons, Inc.
5. Doob J.L. Stochastic Processes (1953), J. Willey & Sons, Inc., Chapman & Hall, New York, Londres
6. Errami M., and Russo F. Covariation de convolution de martingales. C. R. Acad. Sci. Paris Sér. I Math. 326 5 (1998) 601-606
7. Fernique X. Continuité et théorème central limite pour les transformées de Fourier des mesures aléatoires du second ordre. Wahr. Verw. Gebiete 42 (1978) 57-66
8. X. Fernique, Fonctions aléatoires gaussiennes, vecteurs aléatoires gaussiens, Université de Montréal, Centre de Recherches Mathématiques, Montreal, 1997
9. Heath D., Jarrow A., and Morton A. Bond pricing and the term structure of interest rate: a new methodology for contingent claim valuation. Econometrica 60 (1992) 77-105
10. Jain N., and Marcus M.B. Continuity of subgaussian processes. Probability on Banach Spaces. Adv. Probab. vol. 4 (1978), Marcel Dekker, New York 81-196
11. Kahane J.P. Some Random Series of Functions. second ed. (1985), Cambridge Univ. Press, Cambridge
12. Ledoux M., and Talagrand M. Probability in Banach Spaces. Isoperimetry and Processes (1991), Springer-Verlag, New York
13. Marcus M.B. Gaussian lacunary series and the modulus of continuity for Gaussian processes. Z. Wahr. Verw. Gebiete 22 (1972) 301-322
14. Marcus M.B., and Pisier G. Random Fourier Series with Applications to Harmonic Analysis (1981), Princeton Univ. Press
15. Marcus M.B., and Rosiński J. Continuity and boundedness of infinitely divisible processes: a Poisson point process approach. J. Theoret. Probab. 18 (2005) 109-160
16. Pisier G. A remarkable homogeneous Banach algebra. Israel J. Math. 34 (1979) 38-44
17. Protter P. Stochastic Integration and Differential Equations (1990), Springer-Verlag, New York
18. Rosiński J. On path properties of certain infinitely divisible processes. Stochastic Process. Appl. 33 (1989) 73-87
19. Rosiński J. Series representations of Lévy processes from the perspective of point processes. In: Barndorff-Nielsen O.E., Mikosch T., and Resnick S.I. (Eds). Lévy Processes - Theory and Applications (2001), Birkhäuser, Boston 401-415
20. Rosiński J., and Samorodnitsky G. Symmetrization and concentration inequalities for multilinear forms with applications to zero-one laws for Lévy chaos. Ann. Probab. 24 (1996) 422-437