Abstract
This work is an expository article on cylindrical Wiener processes in Banach spaces. We expose the definition of a cylindrical Wiener process as a specific example of a cylindrical process. For that purpose, we gather results on cylindrical Gaussian measures, γ-radonifying operators and cylindrical processes from different sources and relate them to each other. We continue with introducing a stochastic integral with respect to cylindrical Wiener processes but such that the stochastic integral is only a cylindrical random variable. We need not put any geometric constraints on the Banach space under consideration. To this expository work we add a few novel conclusions on the question when a cylindrical Wiener process is a Wiener process in the original sense and on the relation between different stochastic integrals existing in the literature.
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Acknowledgements
I thank David Applebaum for his careful review of the original manuscript and many fruitful discussions.
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© 2011 Springer-Verlag Berlin Heidelberg
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Riedle, M. (2011). Cylindrical Wiener Processes. In: Donati-Martin, C., Lejay, A., Rouault, A. (eds) Séminaire de Probabilités XLIII. Lecture Notes in Mathematics(), vol 2006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15217-7_7
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DOI: https://doi.org/10.1007/978-3-642-15217-7_7
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