Analysis of generalized Lévy white noise functionals

Journal of Functional Analysis

Volumn 211, Issue 1, 2004, Pages 1-70

  Lee, Yuh Jia ^a   Shih, Hsin Hung ^b  

^a NATIONAL UNIVERSITY OF KAOHSIUNG   (Taiwan)

^b KUN SHAN UNIVERSITY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2642578150     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jfa.2003.07.002     Document Type: Article

References (42)

1. S. Albeverio, Yu.L. Daletsky, Yu.G. Kondratiev, L. Streit. Non-Gaussian infinite dimensional analysis, J. Funct. Anal. 138 (1996) 311-350.
2. Y.M. Berezansky, Yu.G. Kondratiev, Spectral Methods in Infinite Dimensional Analysis, Naukova Dumka, Kiev, 1988 (in Russian), English translation, Kluwer Academic Publishers, Dordrecht, 1995.
3. S. Dineen, Complex Analysis on Infinite Dimensional Spaces, Springer, Berlin, 1999.
4. J.L. Doob, Stochastic Processes, Wiley, New York, 1953.
5. I.M. Gel'fand, N.Y. Vilenkin, Generalized Functions, Vol. 4, Academic Press, New York, 1964.
6. T. Hida, Analysis of Brownian Functionals, Carleton Mathematical Lecture Notes 13, 1975.
7. T. Hida, N. Ikeda, Analysis on Hilbert space with reproducing kernel arising from multiple Wiener integral, Proceedings of the 5th Berkeley Symposium on Mathematics Statistics and Probability Vol. II, Part 1, 1967, pp. 117-143.
8. T. Hida, H.-H. Kuo, J. Potthoff, L. Streit, White Noise: An Infinite Dimensional Calculus, Kluwer Academic Publishers, Dordrecht, 1993.
9. K. Itô, Multiple Wiener integral, Japan J. Math. 22 (1952) 157-169.
10. K. Itô, On stochastic processes, Japan J. Math. 18 (1942) 261-301.
11. K. Itô, Spectral type of shift transformations of differential process with stationary increments, Trans. Amer. Math. Soc. 81 (1956) 253-263.
12. Y. Itô, Generalized Poisson functionals, Probab. Theory Related Fields 77 (1988) 1-28.
13. Y. Itô, I. Kubo, Calculus on Gaussian and Poisson White Noises, Nagoya Math. J. 111 (1988) 41-84.
14. G. Kallianpur, Stochastic Filtering Theory, Springer, Berlin, 1980.
15. Yu.G. Kondratiev, E.W. Lytvynov, Operators of gamma white noise spaces, Infinite Dimensional Anal. Quant. Probab. Related Top. 3 (3) (2000) 303-335.
16. Yu.G. Kondratiev, J.L. Silva, L. Streit, G.F. Us, Analysis on Poisson and gamma spaces, Infinite Dimensional Anal. Quant. Probab. Related Top. 1 (1) (1998) 91-118.
17. Yu.G. Kondratiev, L. Streit, W. Westerkamp, J.-A. Yan, Generalized functions in infinite dimensional analysis, Hiroshima Math. J. 28 (1998) 213-260.
18. I. Kubo, S. Takenaka, Calculus on Gaussian white noises I, Proc. Japan Acad. Ser. A Math. Sci. 56 (1980) 376-380;
19. I. Kubo, S. Takenaka, Calculus on Gaussian white noises II, Proc. Japan Acad. Ser. A Math. Sci. 56 (1980) 411-416;
20. I. Kubo, S. Takenaka, Calculus on Gaussian white noises III, Proc. Japan Acad. Ser. A Math. Sci. 57 (1981) 433-437;
21. I. Kubo, S. Takenaka, Calculus on Gaussian white noise IV, Proc. Japan Acad. Ser. A Math. Sci. 58 (1982) 186-189.
22. H.-H. Kuo, White Noise Distribution Theory, CRC Press, Boca Raton, FL, 1996.
23. H.-H. Koo, A. Russek, White noise approach to stochastic integration, J. Multivariate Anal. 24 (1988) 218-236.
24. Y.-J. Lee, Generalized functions on infinite dimensional spaces and its application to white noise calculus, J. Funct. Anal. 82 (1989) 429-464.
25. Y.-J. Lee, Analytic version of test functionals, Fourier transform and a characterization of measures in white noise calculus, J. Funct. Anal. 100 (1991) 359-380.
26. Y.-J. Lee, Integral representation of second quantization and its application to white noise analysis, J. Funct. Anal. 100 (1991) 359-380.
27. Y.-J. Lee, A characterization of generalized functions on infinite dimensional spaces and Bargmann-Segal analytic functions, Gaussian Random Fields, Series on Probability and Statistics, Vol. 1, 1991, pp. 272-284.
28. Y.-J. Lee, H.-H. Shih, The Segal-Bargmann transform for Lévy functionals, J. Funct. Anal. 168 (1999) 46-83.
29. Y.-J. Lee, H.-H. Shih, Donsker's delta function of Lévy processes, Acta Appl. Math. 63 (2000) 219-231.
30. Y.-J. Lee, H.-H. Shih, Itô formula for generalized Lévy functionals, in: T. Hida, K. Saitô (Eds.), Quantum Information II, World Scientific, Singapore, 2000, pp. 87-105.
31. Y.-J. Lee, H.-H. Shih, The product formula of multiple Lévy-Itô integrals, Bull. Inst. Math. Acad. Sinica, (to appear).
32. Y.-J. Lee, H.-H. Shih, A characterization of generalized Lévy functionals, preprint, 2003.
33. E.W. Lytvynov, A. L. Rebenko, G.V. Schepa'nuk, Wick calculus on spaces of generalized functions of compound Poisson white noise, Rep. Math. Phys. 39 (1997) 219-248.
34. P.A. Meyer, Quantum Probability for Probabilists, in: Lecture Notes in Mathematics, Vol. 1538, Springer, Berlin, 1993.
35. N. Obata, White Noise Calculus and Fock Space, in: Lecture Notes in Mathematics, Vol. 1577, Springer, Berlin, 1994.
36. K.R. Parthasarathy, An Introduction to Quantum Stochastic Calculus, Birkauser, Basel/Boston/Berlin, 1992.
37. J. Potthoff, L. Streit, A characterization of Hida distributions, J. Funct. Anal. 101, 212-229.
38. N. Privault, Chaotic and variational calculus in discrete and continuous time for the Poisson process, Stochastic Stochastic Rep. 51 (1-2) (1994) 83-109.
39. N. Privault, A different quantum stochastic calculus for the Poisson process, Probab. Theory Related Fields 105 (1996) 225-278.
40. K. Sato, Lévy Processes and Infinitely Divisible Distributions, Cambridge University Press, Cambridge, 1999.
41. J.L. Silva, Studies in Non-Gaussian Analysis, Ph.D. Dissertation, University of Maderira, 1998.
42. G. Szegö, Orthogonal Polynomials, AMS Colloquium Publication, Vol. 23, American Mathematical Society, Providence, RI, 1939.