Wellposedness of Second Order Backward SDEs
Zhang, Jianfeng; Touzi, Nizar; Soner, Halil Mete (2012), Wellposedness of Second Order Backward SDEs, Probability Theory and Related Fields, 153, 1-2, p. 149-190. http://dx.doi.org/10.1007/s00440-011-0342-y
TypeArticle accepté pour publication ou publié
Journal nameProbability Theory and Related Fields
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CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Soner, Halil Mete
Abstract (EN)We provide an existence and uniqueness theory for an extension of backward SDEs to the second order. While standard Backward SDEs are naturally connected to semilinear PDEs, our second order extension is connected to fully nonlinear PDEs, as suggested in . In particular, we provide a fully nonlinear extension of the Feynman-Kac formula. Unlike , the alternative formulation of this paper insists that the equation must hold under a non-dominated family of mutually singular probability measures. The key argument is a stochastic representation, suggested by the optimal control interpretation, and analyzed in the accompanying paper .
Subjects / Keywordsnon-dominated family of mutually singular measures; Backward SDEs; viscosity solutions for second order PDEs
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