A1 Journal article (refereed)
Decoupling on the Wiener Space, Related Besov Spaces, and Applications to BSDEs (2021)


Geiss, S., & Ylinen, J. (2021). Decoupling on the Wiener Space, Related Besov Spaces, and Applications to BSDEs. Memoirs of the American Mathematical Society, 272(1335), 1-112. https://doi.org/10.1090/memo/1335


JYU authors or editors


Publication details

All authors or editors: Geiss, Stefan; Ylinen, Juha

Journal or series: Memoirs of the American Mathematical Society

ISSN: 0065-9266

eISSN: 1947-6221

Publication year: 2021

Volume: 272

Issue number: 1335

Pages range: 1-112

Publisher: American Mathematical Society

Publication country: United States

Publication language: English

DOI: https://doi.org/10.1090/memo/1335

Publication open access: Not open

Publication channel open access:

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/74282

Publication is parallel published: https://arxiv.org/abs/1409.5322


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.


Keywords: stochastic processes; partial differential equations; functional analysis

Free keywords: Anisotropic Besov spaces; decoupling on the Wiener space; backward stochastic differential equations; interpolation


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Preliminary JUFO rating: 3


Last updated on 2022-17-06 at 10:26