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July 2012 Backward stochastic differential equations with rough drivers
Joscha Diehl, Peter Friz
Ann. Probab. 40(4): 1715-1758 (July 2012). DOI: 10.1214/11-AOP660


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].


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Joscha Diehl. Peter Friz. "Backward stochastic differential equations with rough drivers." Ann. Probab. 40 (4) 1715 - 1758, July 2012.


Published: July 2012
First available in Project Euclid: 4 July 2012

zbMATH: 1259.60057
MathSciNet: MR2978136
Digital Object Identifier: 10.1214/11-AOP660

Primary: 60H10 , 60H15

Keywords: backward doubly stochastic differential equations , Backward stochastic differential equations , rough path analysis , Stochastic partial differential equations , viscosity theory

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.40 • No. 4 • July 2012
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