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- W4297571813 abstract "As an extension of the Doob-Meyer decomposition of a semimartingale and the Fukushima representation of a Dirichlet process, we introduce a general Doob decomposition in continuous time, where a square-integrable process is represented as the sum of a martingale and a process with “vanishing local risk”. For a probability measure Q on Wiener space, we discuss how entropy conditions on Q formulated with respect to Wiener measure P are connected with the Doob decomposition of the coordinate process W under Q. The situation is well understood if the relative entropy H(Q|P) is finite; in this case the decomposition is classical and yields an immediate proof of Talagrand’s transport inequality on Wiener space. To go beyond this restriction, we consider the specific relative entropy h(Q|P) on Wiener space that was introduced by Gantert in [11]. We discuss its interplay with the Doob decomposition of W under Q and a corresponding version of Talagrand’s inequality, with special emphasis on the case where W is a Dirichlet process under Q." @default.
- W4297571813 created "2022-09-29" @default.
- W4297571813 creator A5086713369 @default.
- W4297571813 date "2022-01-01" @default.
- W4297571813 modified "2023-10-14" @default.
- W4297571813 title "Doob Decomposition, Dirichlet Processes, and Entropies on Wiener Space" @default.
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- W4297571813 doi "https://doi.org/10.1007/978-981-19-4672-1_8" @default.
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