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Lévy noises and stochastic integrals on Banach spaces. (English) Zbl 1096.60024
Da Prato, Giuseppe (ed.) et al., Stochastic partial differential equations and applications – VII. Papers of the 7th meeting, Levico, Terme, Italy, January 5–10, 2004. Boca Raton, FL: Chapman & Hall/CRC (ISBN 0-8247-0027-9/pbk). Lecture Notes in Pure and Applied Mathematics 245, 193-213 (2006).
This paper reviews previous work by the second author on Lévy white noise on Banach spaces and provides an extended notion of the associated stochastic integral, now with respect to martingale integrators on Banach spaces. It is also shown how perpetuities in insurance can be computed in an exponential (real-valued) Lévy model as the invariant measure of a Markov process. The text contains some elementary mistakes in the calculations (see the end of the proof of Theorem 17.9) which do not affect the main results.
For the entire collection see [Zbl 1079.60009].

60G51 Processes with independent increments; Lévy processes
60H05 Stochastic integrals
46B09 Probabilistic methods in Banach space theory
91B30 Risk theory, insurance (MSC2010)