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Decoupling on the Wiener Space, Related Besov Spaces, and Applications to BSDEs: 272 (Memoirs of the American Mathematical Society)

Mathematical Analysis

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We introduce a decoupling method on the Wiener space to define a wide class of anisotropic Besov spaces. The decoupling method is based on a general distributional approach and not restricted to the Wiener space. The class of Besov spaces we introduce contains the traditional isotropic Besov spaces obtained by the real interpolation method, but also new spaces that are designed to investigate backwards stochastic differential equations (BSDEs). As examples we discuss the Besov regularity (in the sense of our spaces) of forward diffusions and local times. It is shown that among our newly introduced Besov spaces there are spaces that characterize quantitative properties of directional derivatives in the Malliavin sense without computing or accessing these Malliavin derivatives explicitly. Regarding BSDEs, we deduce regularity properties of the solution processes from the Besov regularityof the initial data, in particular upper bounds for their Lp-variation, where the generator might be of quadratic type and where no structural assumptions, for example in terms of aforward diffusion, are assumed. As an example we treat sub-quadratic BSDEs with unbounded terminal conditions. Among other tools, we use methods from harmonic analysis. As a by-product, we improve the asymptotic behaviour of the multiplicative constant in a generalized Fefferman inequality and verify the optimality of the bound we established.

Product Specifications

Format: paperback
ASIN: 1470449358
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Mathematical Analysis
Domain: Amazon UK
Release Date: 30 March 2022
Listed Since: 30 November 2021

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Decoupling on the Wiener Space, Related Besov Spaces, and Applications to BSDEs: 272 (Memoirs of the American Mathematical Society)

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