A chaotic decomposition for generalized stochastic processes with independent values

• Autorzy: Das S. , Lytvynov E.
• Języki publikacji: EN

Abstrakty

EN

We extend the result of Nualart and Schoutens on chaotic decomposition of the L²-space of a Lévy process to the case of a generalized stochastic processes with independent values.

Słowa kluczowe

EN

chaotic decomposition; generalized stochastic process; Lévy proces

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2013
• Tom: Vol. 33, Fasc. 2
• Strony: 409--423
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Das S.

• Swansea University, Department of Mathematics, Singleton Park, Swansea, SA2 8PP, U.K.

autor

Lytvynov E.

• Swansea University, Department of Mathematics, Singleton Park, Swansea, SA2 8PP, U.K.

Bibliografia

• [1] M. Anshelevich, q-Lévy processes, J. Reine Angew. Math. 576 (2004), pp. 81-207.
• [2] Y. M. Berezansky and Y. G. Kondratiev, Spectral Methods in Infinite-Dimensional Analysis. Vol. 1, Kluwer Academic Publishers, Dordrecht 1995.
• [3] M. Bożejko and E. Lytvynov, Meixner class of non-commutative generalized stochastic processes with freely independent values. I. A characterization, Comm. Math. Phys. 292 (2009), pp. 99-129.
• [4] T. S. Chihara, An Introduction to Orthogonal Polynomials, Math. Appl., Vol. 13, Gordon and Breach Science Publishers, New York-London-Paris 1978.
• [5] S. Das, Orthogonal Decompositions for Generalized Stochastic Processes with Independent Values, PhD thesis, Swansea 2013.
• [6] G. Di Nunno, B. Øksendal, and F. Proske, Malliavin Calculus for Lévy Processes with Applications to Finance, Universitext, Springer, Berlin 2009.
• [7] J. Lin, Chaotic and predictable representations for multidimensional Lévy processes, arXiv preprint, 2011.
• [8] E. Lytvynov, Orthogonal decompositions for Lévy processes with an application to the gamma, Pascal, and Meixner processes, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 6 (2003), pp. 73-102.
• [9] D. Nualart and W. Schoutens, Chaotic and predictable representations for Lévy processes, Stochastic Process. Appl. 90 (2000), pp. 109-122.
• [10] W. Schoutens, Stochastic Processes and Orthogonal Polynomials, Lecture Notes in Statist., Vol. 146, Springer, New York 2000.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).