The construction of the chaotic representation for the gamma field

Infinite Dimensional Analysis, Quantum Probability and Related Topics

Volumn 6, Issue 1, 2003, Pages 33-56

  Berezansky, Yurij M ^a   Mierzejewski, Dmytro A ^a  

^a INSTITUTE OF MATHEMATICS   (Ukraine)

Author keywords

Chaotic representation; Gamma process; Jacobi field

Indexed keywords

EID: 0038363409     PISSN: 02190257     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219025703001043     Document Type: Article

References (23)

1. Yu. M. Berezansky, Spectral approach to white noise analysis, in Dynamics of Complex and Irregular Systems, Proc. of Symp., 16-20 December 1991, Germany) Bielefeld Encounters in Math. and Phys., VIII (World Scientific, 1993), pp. 131-140.
2. Yu. M. Berezansky, On the theory of commutative Jacobi fields, Methods Funct. Anal. Topol. 4 (1998), No. 1, 1-31.
3. Yu. M. Berezansky, Commutative Jacobi fields in Fock space, Integr. Equ. Oper. Theory 30 (1998) 163-190.
4. Yu. M. Berezansky, On the direct and inverse spectral problems for Jacobi fields, St. Petersburg Math. J. 9 (1998) 1053-1071.
5. Yu. M. Berezansky, Spectral theory of commutative Jacobi fields: Direct and inverse problems, Fields Inst. Commun. 25 (2000) 211-224.
6. Yu. M. Berezansky and Yu. G. Kondratiev, Spectral Methods in Infinite-Dimensional Analysis (Kluwer, 1995), Vols. 1 and 2.
7. Yu. M. Berezansky, V. O. Livinsky and E. W. Lytvynov, A generalization of Gaussian white noise analysis, Methods Funct. Anal. Topol. 1 (1995), No. 1, 28-55.
8. Yu. M. Berezansky and D. A. Mierzejewski, The structure of the extended symmetric Fock space, Methods Funct. Anal. Topol. 6 (2000), No. 4, 1-13.
9. Yu. M. Berezansky and D. A. Mierzejewski The chaotic decomposition for the Gamma field, Funct. Anal. Appl. 35 (2001) 305-308.
10. Yu. M. Berezansky, Z. G. Sheftel and G. F. Us, Functional Analysis (Birkhäuser, 1996), Vols. 1 and 2.
11. A. Dermoune, Distributions sur l'espace de P. Lévy et calcul stochastique, Ann. Inst. Henri Poincaré 26 (1990), No. 1, 101-119.
12. I. I. Gikhman and A. V. Skorokhod, The Theory of Random Processes (in Russian) (Nauka, 1975), Vol. 3.
13. T. Hida, Brownian Motion (Springer, 1980).
14. N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion Processes (North-Holland, 1981).
15. Yu. G. Kondratiev and E. W. Lytvynov, Operators of Gamma white noise calculus, Infinite Dim. Anal. Quantum Probab. Related Topics 3 (2000) 303-335.
16. Yu. G. Kondratiev, J. L. Da Silva, L. Streit and G. F. Us, Analysis on Poisson and Gamma spaces, Infinite Dim. Anal. Quantum Probab. Related Topics 1 (1998) 91-117.
17. E. W. Lytvynov, Multiple Wiener integrals and non-Gaussian white noises: A Jacobi field approach, Methods Funct. Anal. Topol. 1 (1995), No. 1, 61-85.
18. D. Nualart and W. Schoutens, Chaotic and predictable representations for Lévy processes, Stoch. Processes Appl. 90 (2000) 109-122.
19. N. Obata, White Noise Calculus and Fock Space (Springer, 1994).
20. P. Protter, Stochastic Integration and Differential Equations (Springer, 1990).
21. W. Schoutens, Stochastic Processes and Orthogonal Polynomials (Springer, 2000).
22. L. Takács, Combinatorial Methods in the Theory of Stochastic Processes (John Wiley & Sons, 1967).
23. A. D. Wentzell, Theorie Zufälliger Prozesse (Akademie-Verlag, 1979).