02659nam 22005532 450 991048006930332120201123142619.01-64189-916-61-64189-083-510.1515/9781641890830(CKB)4100000008780952(MiAaPQ)EBC5841217(DE-B1597)541572(OCoLC)1104741803(DE-B1597)9781641890830(UkCbUP)CR9781641890830(EXLCZ)99410000000878095220201011d2019|||| uy| 0engur|||||||||||txtrdacontentcrdamediacrrdacarrierMedieval Islamic sectarianism /Christine D. Baker[electronic resource]Leeds :Arc Humanities Press,2019.1 online resource (x, 106 pages) digital, PDF file(s)Past imperfectTitle from publisher's bibliographic system (viewed on 20 Nov 2020).1-64189-082-7 Front matter --Contents --Acknowledgements and a Note on Transliteration --Timeline --Introduction --Chapter 1. When did Sunnism Become Orthodox? --Chapter 2. Non-Sunni Islams Before the Tenth Century --Chapter 3. The Fatimids and Isma'ili Shi'ism in North Africa --Chapter 4. The Buyids and Shiʿism in Baghdad --Conclusion: Reactions to the Shiʿi Century --Glossary of Key Terms --Further ReadingThis book asks readers to re-examine their view of the Islamic world and the development of sectarianism in the Middle East by shining a light on the complexity and diversity of early Islamic society. While Sunni Islam eventually became politically and numerically dominant, Sunni and Shiʿi identities took centuries to develop as independent communities. When modern discussions of sectarianism in the Middle East reduce these identities to a 1400-year war between Sunnis and Shiʿis, we create a false narrative.Past imperfect (ARC Humanities Press)IslamMiddle EastHistoryTo 1500SunnitesRelationsShīʻahShīʻahRelationsSunnitesIslamRelationsMiddle EastReligionIslamHistorySunnitesRelationsShīʻah.ShīʻahRelationsSunnites.IslamRelations.297.804209560902Baker Christine D.282710UkCbUPUkCbUPBOOK9910480069303321Medieval Islamic sectarianism2457378UNINA05309nam 22006253 450 991095881110332120231110215859.097814704675171470467518(CKB)4940000000616393(MiAaPQ)EBC6798082(Au-PeEL)EBL6798082(RPAM)22488145(PPN)259970794(OCoLC)1275392940(EXLCZ)99494000000061639320211214d2021 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierDecoupling on the Wiener Space, Related Besov Spaces, and Applications to BSDEs1st ed.Providence :American Mathematical Society,2021.©2021.1 online resource (124 pages)Memoirs of the American Mathematical Society ;v.2729781470449353 1470449358 Includes bibliographical references and index.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 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."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.Memoirs of the American Mathematical Society Stochastic differential equationsBesov spacesProbability theory and stochastic processes -- Stochastic analysis -- Stochastic calculus of variations and the Malliavin calculusmscProbability theory and stochastic processes -- Stochastic analysis -- Stochastic ordinary differential equationsmscFunctional analysis -- Linear function spaces and their duals -- Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theoremsmscStochastic 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.519.2/260H0760H1046E35mscGeiss Stefan1799909Ylinen Juha1799910MiAaPQMiAaPQMiAaPQBOOK9910958811103321Decoupling on the Wiener Space, Related Besov Spaces, and Applications to BSDEs4344338UNINA