A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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-tekijät tai -toimittajat


Julkaisun tiedot

Julkaisun kaikki tekijät tai toimittajat: Geiss, Stefan; Ylinen, Juha

Lehti tai sarja: Memoirs of the American Mathematical Society

ISSN: 0065-9266

eISSN: 1947-6221

Julkaisuvuosi: 2021

Volyymi: 272

Lehden numero: 1335

Artikkelin sivunumerot: 1-112

Kustantaja: American Mathematical Society

Julkaisumaa: Yhdysvallat (USA)

Julkaisun kieli: englanti

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

Julkaisun avoin saatavuus: Ei avoin

Julkaisukanavan avoin saatavuus: 

Julkaisu on rinnakkaistallennettu (JYX): https://jyx.jyu.fi/handle/123456789/74282

Julkaisu on rinnakkaistallennettu: https://arxiv.org/abs/1409.5322


Tiivistelmä

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.


YSO-asiasanat: stokastiset prosessit; osittaisdifferentiaaliyhtälöt; funktionaalianalyysi

Vapaat asiasanat: Anisotropic Besov spaces; decoupling on the Wiener space; backward stochastic differential equations; interpolation


Liittyvät organisaatiot


OKM-raportointi: Kyllä

Raportointivuosi: 2021

JUFO-taso: 3


Viimeisin päivitys 2024-03-04 klo 20:26