Articlegreen2012

Backward stochastic differential equations with rough drivers

34 citations0/0 files storedThe Annals of Probability

No readable copy stored yet — this record is metadata only.

No open-access location is known for this record yet.

Literature note Cite in a project Citation map

Stochastic processes and financial applications Nonlinear Differential Equations Analysis Fuzzy Systems and Optimization

Abstract

Backward stochastic differential equations (BSDEs) in the sense of Pardoux–Peng [Lecture Notes in Control and Inform. Sci. 176 (1992) 200–217] provide a non-Markovian extension to certain classes of nonlinear partial differential equations; the nonlinearity is expressed in the so-called driver of the BSDE. Our aim is to deal with drivers which have very little regularity in time. To this end, we establish continuity of BSDE solutions with respect to rough path metrics in the sense of Lyons [Rev. Mat. Iberoam. 14 (1998) 215–310] and so obtain a notion of “BSDE with rough driver.” Existence, uniqueness and a version of Lyons’ limit theorem in this context are established. Our main tool, aside from rough path analysis, is the stability theory for quadratic BSDEs due to Kobylanski [Ann. Probab. 28 (2000) 558–602].

Paper brief

Loading…

Cite this work

Citation unavailable for this work.

BibTeX RIS CSL-JSON

No public copy is stored for this record, so only the metadata is cited.

Citations in this library

Citation map →

Stored only when both papers are in the corpus — 34 citations exist upstream.

References

1990Adapted solution of a backward stochastic differential equation 1997Backward Stochastic Differential Equations in Finance 2000Backward stochastic differential equations and partial differential equations with quadratic growth 2010Multidimensional Stochastic Processes as Rough Paths 1997Backward stochastic differential equations and integral-partial differential equations 2002System Control and Rough Paths 2007Differential Equations Driven by Rough Paths 1994Backward doubly stochastic differential equations and systems of quasilinear SPDEs

Cited by

2020Backward doubly stochastic Volterra integral equations and their applications 2017Stochastic partial differential equations: a rough paths view on weak solutions via Feynman–Kac

Explore the map →

Papers that cite the same references — the relational fallback while embeddings are still backfilling.

Imported from OpenAlex (CC0) — nothing here is generated.