LEADER 05309nam 22006253 450 001 9910958811103321 005 20231110215859.0 010 $a9781470467517 010 $a1470467518 035 $a(CKB)4940000000616393 035 $a(MiAaPQ)EBC6798082 035 $a(Au-PeEL)EBL6798082 035 $a(RPAM)22488145 035 $a(PPN)259970794 035 $a(OCoLC)1275392940 035 $a(EXLCZ)994940000000616393 100 $a20211214d2021 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aDecoupling on the Wiener Space, Related Besov Spaces, and Applications to BSDEs 205 $a1st ed. 210 1$aProvidence :$cAmerican Mathematical Society,$d2021. 210 4$d©2021. 215 $a1 online resource (124 pages) 225 1 $aMemoirs of the American Mathematical Society ;$vv.272 311 08$a9781470449353 311 08$a1470449358 320 $aIncludes bibliographical references and index. 327 $aCover -- 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_{ }^{??} -- 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 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. 330 $a"We introduce a decoupling method on the Wiener space to define a wide class of anisotropic Besov spaces. The decoupling method is based on a general distributional approach and not restricted to the Wiener space. The class of Besov spaces we introduce contains the traditional isotropic Besov spaces obtained by the real interpolation method, but also new spaces that are designed to investigate backwards stochastic differential equations (BSDEs). As examples we discuss the Besov regularity (in the sense of our spaces) of forward diffusions and local times. It is shown that among our newly introduced Besov spaces there are spaces that characterize quantitative properties of directional derivatives in the Malliavin sense without computing or accessing these Malliavin derivatives explicitly. Regarding BSDEs, we deduce regularity properties of the solution processes from the Besov regularity of the initial data, in particular upper bounds for their Lpvariation, where the generator might be of quadratic type and where no structural assumptions, for example in terms of a forward diffusion, are assumed. As an example we treat sub-quadratic BSDEs with unbounded terminal conditions. Among other tools, we use methods from harmonic analysis. As a by-product, we improve the asymptotic behaviour of the multiplicative constant in a generalized Fefferman inequality and verify the optimality of the bound we established"--$cProvided by publisher. 410 0$aMemoirs of the American Mathematical Society 606 $aStochastic differential equations 606 $aBesov spaces 606 $aProbability theory and stochastic processes -- Stochastic analysis -- Stochastic calculus of variations and the Malliavin calculus$2msc 606 $aProbability theory and stochastic processes -- Stochastic analysis -- Stochastic ordinary differential equations$2msc 606 $aFunctional analysis -- Linear function spaces and their duals -- Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems$2msc 615 0$aStochastic differential equations. 615 0$aBesov spaces. 615 7$aProbability theory and stochastic processes -- Stochastic analysis -- Stochastic calculus of variations and the Malliavin calculus. 615 7$aProbability theory and stochastic processes -- Stochastic analysis -- Stochastic ordinary differential equations. 615 7$aFunctional analysis -- Linear function spaces and their duals -- Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems. 676 $a519.2/2 686 $a60H07$a60H10$a46E35$2msc 700 $aGeiss$b Stefan$01799909 701 $aYlinen$b Juha$01799910 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910958811103321 996 $aDecoupling on the Wiener Space, Related Besov Spaces, and Applications to BSDEs$94344338 997 $aUNINA