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Record Nr. |
UNINA9910958811103321 |
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Autore |
Geiss Stefan |
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Titolo |
Decoupling on the Wiener Space, Related Besov Spaces, and Applications to BSDEs |
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Pubbl/distr/stampa |
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Providence : , : American Mathematical Society, , 2021 |
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©2021 |
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ISBN |
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Edizione |
[1st ed.] |
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Descrizione fisica |
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1 online resource (124 pages) |
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Collana |
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Memoirs of the American Mathematical Society ; ; v.272 |
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Classificazione |
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Altri autori (Persone) |
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Disciplina |
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Soggetti |
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Stochastic differential equations |
Besov spaces |
Probability theory and stochastic processes -- Stochastic analysis -- Stochastic calculus of variations and the Malliavin calculus |
Probability theory and stochastic processes -- Stochastic analysis -- Stochastic ordinary differential equations |
Functional analysis -- Linear function spaces and their duals -- Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Cover -- Title page -- Chapter 1. Introduction -- 1.1. Background -- 1.2. Outline of the main ideas -- 1.3. Notation -- Chapter 2. A General Factorization -- 2.1. The operators \C and \C^{ } -- 2.2. The operators \C and \C^{ } for stochastic processes -- Chapter 3. Transference of SDEs -- 3.1. Setting -- 3.2. Results -- Chapter 4. Anisotropic Besov Spaces on the Wiener Space -- 4.1. Classical Besov spaces on the Wiener space -- 4.2. Setting -- 4.3. Definition of anisotropic Besov spaces -- 4.4. Connection to real interpolation -- 4.5. The space \B_{ }^{Φ₂} -- 4.6. An embedding theorem for functionals of bounded variation -- 4.7. Examples -- Chapter 5. Continuous BMO-Martingales -- 5.1. Continuous BMO-martingales and sliceable numbers -- 5.2. Fefferman's inequality and \bmo( _{2 }) spaces -- 5.3. Reverse Hölder inequalities -- 5.4. An application to BSDEs -- Chapter 6. Applications to BSDEs -- 6.1. The setting -- 6.2. Stability of BSDEs with respect to |
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perturbations of the Gaussian structure -- 6.3. On classes of quadratic and sub-quadratic BSDEs -- 6.4. Settings for the stability theorem -- 6.5. On the _{ }-variation of BSDEs -- 6.6. Applications to other types of BSDEs -- Appendix A. Technical Facts -- Bibliography -- Index -- Back Cover. |
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Sommario/riassunto |
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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 regularity of the initial data, in particular upper bounds for their Lpvariation, where the generator might be of quadratic type and where no structural assumptions, for example in terms of a forward 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"-- |
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