Analysis on poisson and gamma spaces

Infinite Dimensional Analysis, Quantum Probability and Related Topics

Volumn 1, Issue 1, 1998, Pages 91-117

  Kondratiev, Yuri G ^a,b,c   Da Silva, José L ^a,d   Streit, Ludwig ^a,d   Us, Georgi F ^e  

^a BIELEFELD UNIVERSITY   (Germany)

^b INSTITUTE OF MATHEMATICS   (Ukraine)

^c UNIVERSITY OF BONN   (Germany)

^d UNIVERSITY OF MADEIRA   (Portugal)

^e TARAS SHEVCHENKO NATIONAL UNIVERSITY OF KYIV   (Ukraine)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 3042891710     PISSN: 02190257     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219025798000089     Document Type: Article

References (29)

1. Eds. S. Albeverio, Ph. Blanchard and D. Testard, Stochastics, Algebra and Analysis in Classical and Quantum Dynamics, Math. Appl. (Kluwer, 1990).
2. S. Albeverio and J.-L. Wu, Euclidean random fields obtained by convolution from generalized white noise, J. Math. Phys. 36 (1995) 5217-5245.
3. Yu. M. Berezansky and Yu. G. Kondratiev, Spectral Methods in Infinite-Dimensional analysis (Kluwer, 1995) (in Russian, Naukova Dumka, 1988).
4. N. Bourbaki, Functions d'une Variable Réele (Théorie Élémentaire). Éléments de Mathématique Livre IV (Hermann et Cie, 1950).
5. E. Carlen and E. Pardoux, Differential calculus and integration by parts on Poisson space, in Ref. 1, pp. 63-73.
6. A. Dermoune, Distributions sur l'espace de P. Lévy et calcul stochastique, Ann. Inst. H. Poincaré Probab. Statist. 26 (1990) 101-119.
7. I. M. Gel'fand, M. I. Graev and A. M. Vershik, Representations of the group of diffeomorphisms, Russian Math. Surveys 30 (1975) 3-50.
8. I. Gradstein and I. Ryshik, Table of Series, Products and Integrals (Verlag Harri Deutsch Thun, 1981), Vol. 1.
9. A. Guichardet, Symmetric Hilbert Spaces and Related Topics, Lecture Notes in Mathematics (Springer-Verlag, 1972).
10. I. M. Gel'fand and N. Ya. Vilenkin, Generalized Functions (Academic Press, 1968), Vol. IV.
11. T. Hida, H. H. Kuo, J. Potthoff and L. Streit, White Noise. An Infinite Dimensional Calculus (Kluwer, 1993).
12. Y. Ito and I. Kubo, Calculus on Gaussian and Poisson white noises Nagoya Math. J. 111 (1988) 41-84.
13. K. Ito, Spectral type of the shift transformation of differential processes with stationary increments, Trans. Amer. Math. Soc. 81 (1956) 253-263.
14. O. Kallenberg, Lectures on Random Measures (University of North Carolina, 1974).
15. O. Kallenberg, Random Measures (Akademie-Verlag, 1983), 3rd edition.
16. J. Kerstan, K. Matthes and J. Mecke, Infinite Divisible Point Processes (Akademie-Verlag, 1978).
17. T. Kailath and A. Segall, Orthogonal functionals of independent increment processes, IEEE Trans. Inform. Theory 22 (1976) 287-298.
18. Yu. G. Kondratiev, J. L. Silva and L. Streit, Generalized appell systems, Methods Funct. Anal. Topology 3, No. 3 (1997).
19. E. W. Lytvynov, A. L. Rebenko and G. V. Shchepa'nuk, Wick calculus on spaces of generalized functions of compound Poisson and white noise, Rep. Math. Phys. 39 (1997) 219-248.
20. J. Mecke, Stationäre zufällige maße auf lokalkompakten abelschen gruppen, Z. Wahrscheinlichkeitstheorie und verw. Gebiete 9 (1967) 36-58.
21. P. A. Meyer, Quantum Probability for Probabilists, Lecture Notes in Math. (Springer, 1993), Vol. 1583.
22. D. Nualart and J. Vives, A duality formula on the Poisson space and some applications, preprint, Univ. Barcelona, 1995.
23. X. X. Nguyen and H. Zessin, Punktprozesse mit wechselwickung, Z. Wahrscheinlichkeitstheorie und verw. Gebiete 37 (1976) 91-126.
24. N. Privault, A transfer principle from Wiener to Poisson space and applications, J. Funct. Anal. 132 (1995) 335-360.
25. E. D. Rainville, Special Functions (Chelsea 1971).
26. M. Reed and B. Simon, Methods of Modern Mathematical Physics (Academic Press, 1975), Vol. II.
27. A. V. Skorohod, On the differentiability of measures which correspond to stochastic processes I. processes with independent increments, Theory Probab. Appl. II (1957) 407-423.
28. L. Takács, Combinatorial Methods in the Theory of Stochastic Processes (John Wiley & Sons, 1967).
29. Y. Takahashi, Absolute continuity of Poisson random fields, Publ. Res. Inst. Math. Sci. 26 (1990) 629-649.