Girsanov theory under a finite entropy condition
By Christian Léonard. 2011
53 citations recorded by the source corpus.
This paper is about Girsanov’s theory. It (almost) doesn’t contain new results but it is based on a simplified new approach which takes advantage of the (weak) extra requirement that some relative entropy is finite. Under this assumption, we present and prove all the standard results pertaining to the absolute continuity of two continuous-time processes on \({\mathbb{R}}^{d}\) with or without jumps. We have tried to give as much as possible a self-contained presentation. The main advantage of the finite entropy strategy is that it allows us to replace martingale representation results by the simpler Riesz representations of the dual of a Hilbert space (in the continuous case) or of an Orlicz function space (in the jump case).
Subfields: Control and Systems Engineering, Finance, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/8e1b7492b2d8f0f4177311f866901801f52ccdef
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In Finance
In Statistical and Nonlinear Physics
Citations in the corpus
- A survey of the Schr\"odinger problem and some of its connections with optimal transport (2013, background): “For a proof with an analytic flavour, see for instance [Léo12b].”
- Time reversal of diffusion processes under a finite entropy condition (2021, unknown): “1) We know by the Girsanov theory under a finite entropy condition [30], that when R fulfils the uniqueness condition: ∀R′ ∈ M(Ω), [R′ ∈ MP(R0, a, b) and R′ R] =⇒ R′ = R, (4.”
- Riemannian Score-Based Generative Modeling (2022, unknown): “To circumvent this problem, one can consider a process whose initial and terminal distribution are pinned down using Schrödinger bridges (Schrödinger, 1932; Léonard, 2012a; Chen et al., 2016; De Bortoli et al., 2021; Vargas et al., 2021).”