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010 a| 2022007967;

020 a| 9781470449353q| (paperback);

020 z| 9781470467517q| (epub);

035 a| (WaSeSS)ssj0002593372;

042 a| pcc;

049 a| EREEa| NEHH;

050 00 a| QA274.23b| .G45 2021;

082 00 a| 519.2/22| 23/eng20220502;

084 a| 60H07a| 60H10a| 46E352| msc;

100 1 a| Geiss, Stefan,d| 1958-?| UNAUTHORIZED;

245 10 a| Decoupling on the Wiener space, related Besov spaces, and applications to BSDEsh| [electronic resource] /c| Stefan Geiss, Juha Ylinen.;

260 a| Providence :b| American Mathematical Society,c| [2021];

300 a| v, 112 pages ;c| 26 cm;

490 0 a| Memoirs of the American Mathematical Society,x| 0065-9266 ;v| Volume 272, Number 1335 (fifth of 7 numbers);

504 a| Includes bibliographical references and index.;

506 a| Available only to authorized users.;

520 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"--c| Provided by publisher.;

538 a| Mode of access: World Wide Web;

650 0 a| Stochastic differential equations.=| ^A69732;

650 0 a| Besov spaces.=| ^A67375;

650 7 a| Probability theory and stochastic processes -- Stochastic analysis -- Stochastic calculus of variations and the Malliavin calculus.2| msc;

650 7 a| Probability theory and stochastic processes -- Stochastic analysis -- Stochastic ordinary differential equations.2| msc;

650 7 a| Functional analysis -- Linear function spaces and their duals -- Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems.2| msc;

655 0 a| Electronic books.=| ^A491897;

700 1 a| Ylinen, Juha.?| UNAUTHORIZED;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=6798082;

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Decoupling on the Wiener space, related Besov spaces, and applications to BSDEs / Stefan Geiss, Juha Ylinen.

Author/creator	Geiss, Stefan, 1958-
Other author	Ylinen, Juha.
Format	Electronic
Publication Info	Providence : American Mathematical Society, [2021]
Description	v, 112 pages ; 26 cm
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	Stochastic differential equations. Besov spaces.

Series	Memoirs of the American Mathematical Society, 0065-9266 ; Volume 272, Number 1335 (fifth of 7 numbers)
Abstract	"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"-- Provided by publisher.
Bibliography note	Includes bibliographical references and index.
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2022007967
ISBN	9781470449353 (paperback)
ISBN	(epub)

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Decoupling on the Wiener space, related Besov spaces, and applications to BSDEs / Stefan Geiss, Juha Ylinen.

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