Journal Articles Probability Surveys Year : 2023

Elementary processes for Itô Integral against cylindrical Wiener process

Abstract

In this article, I present different definitions of elementary processes which lead to definitions of Itô integrals against cylindrical Wiener processes. I prove the equivalence between those definitions by constructing this Itô integral using only Itô isometries and extensions by density. Then, from the perspective of white noise theory and Kondratiev spaces, I compare the definitions of cylindrical Wiener processes, and present a link between Itô integral and cylindrical white noise.
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hal-04489829 , version 1 (05-03-2024)

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Sylvain Dotti. Elementary processes for Itô Integral against cylindrical Wiener process. Probability Surveys, 2023, 20, ⟨10.1214/23-ps23⟩. ⟨hal-04489829⟩
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