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Stochastic integration for Lévy processes with values in Banach spaces

Author

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  • Riedle, Markus
  • van Gaans, Onno

Abstract

A stochastic integral of Banach space valued deterministic functions with respect to Banach space valued Lévy processes is defined. There are no conditions on the Banach spaces or on the Lévy processes. The integral is defined analogously to the Pettis integral. The integrability of a function is characterized by means of a radonifying property of an integral operator associated with the integrand. The integral is used to prove a Lévy-Itô decomposition for Banach space valued Lévy processes and to study existence and uniqueness of solutions of stochastic Cauchy problems driven by Lévy processes.

Suggested Citation

  • Riedle, Markus & van Gaans, Onno, 2009. "Stochastic integration for Lévy processes with values in Banach spaces," Stochastic Processes and their Applications, Elsevier, vol. 119(6), pages 1952-1974, June.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:6:p:1952-1974
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    Citations

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    Cited by:

    1. C. A. Fonseca-Mora, 2020. "Lévy Processes and Infinitely Divisible Measures in the Dual of a Nuclear Space," Journal of Theoretical Probability, Springer, vol. 33(2), pages 649-691, June.
    2. Nelson Vadori & Anatoliy Swishchuk, 2019. "Inhomogeneous Random Evolutions: Limit Theorems and Financial Applications," Mathematics, MDPI, vol. 7(5), pages 1-62, May.
    3. Issoglio, E. & Riedle, M., 2014. "Cylindrical fractional Brownian motion in Banach spaces," Stochastic Processes and their Applications, Elsevier, vol. 124(11), pages 3507-3534.

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