Generalized fractional smoothness and L p-variation of BSDEs with non-Lipschitz terminal condition

Christel Geiss; Stefan Geiss; Emmanuel Gobet

doi:10.1016/j.spa.2012.02.006

Generalized fractional smoothness and L _p-variation of BSDEs with non-Lipschitz terminal condition

Christel Geiss
, Stefan Geiss
, Emmanuel Gobet

Department of Mathematics
University of Innsbruck

Research output: Contribution to journal › Article › peer-review

30 Citations (Scopus)

Abstract

We relate the L _p-variation, 2≤p<∞, of a solution of a backward stochastic differential equation with a path-dependent terminal condition to a generalized notion of fractional smoothness. This concept of fractional smoothness takes into account the quantitative propagation of singularities in time.

Original language	English
Pages (from-to)	2078-2116
Number of pages	39
Journal	Stochastic Processes and their Applications
Volume	122
Issue number	5
DOIs	https://doi.org/10.1016/j.spa.2012.02.006
Publication status	Published - 1 May 2012

Keywords

Backward stochastic differential equation
Besov spaces
Fractional smoothness
Lp -variation

Access to Document

10.1016/j.spa.2012.02.006

Cite this

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title = "Generalized fractional smoothness and L p-variation of BSDEs with non-Lipschitz terminal condition",

abstract = "We relate the L p-variation, 2≤p<∞, of a solution of a backward stochastic differential equation with a path-dependent terminal condition to a generalized notion of fractional smoothness. This concept of fractional smoothness takes into account the quantitative propagation of singularities in time.",

keywords = "Backward stochastic differential equation, Besov spaces, Fractional smoothness, Lp -variation",

author = "Christel Geiss and Stefan Geiss and Emmanuel Gobet",

year = "2012",

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T1 - Generalized fractional smoothness and L p-variation of BSDEs with non-Lipschitz terminal condition

AU - Geiss, Christel

AU - Geiss, Stefan

AU - Gobet, Emmanuel

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Y1 - 2012/5/1

N2 - We relate the L p-variation, 2≤p<∞, of a solution of a backward stochastic differential equation with a path-dependent terminal condition to a generalized notion of fractional smoothness. This concept of fractional smoothness takes into account the quantitative propagation of singularities in time.

AB - We relate the L p-variation, 2≤p<∞, of a solution of a backward stochastic differential equation with a path-dependent terminal condition to a generalized notion of fractional smoothness. This concept of fractional smoothness takes into account the quantitative propagation of singularities in time.

KW - Backward stochastic differential equation

KW - Besov spaces

KW - Fractional smoothness

KW - Lp -variation

U2 - 10.1016/j.spa.2012.02.006

DO - 10.1016/j.spa.2012.02.006

M3 - Article

AN - SCOPUS:84860528406

SN - 0304-4149

VL - 122

SP - 2078

EP - 2116

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 5