Mean-Field Backward Stochastic Differential Equations and Related Partial Differential Equations

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dc.creatorBuckdahn, Rainer
dc.creatorLi, Juan
dc.creatorPeng, Shige
dc.date2007-11-14
dc.date.accessioned2026-07-07T08:43:54Z
dc.date.available2026-07-07T08:43:54Z
dc.descriptionIn [5] the authors obtained Mean-Field backward stochastic differential equations (BSDE) associated with a Mean-field stochastic differential equation (SDE) in a natural way as limit of some highly dimensional system of forward and backward SDEs, corresponding to a large number of ``particles'' (or ``agents''). The objective of the present paper is to deepen the investigation of such Mean-Field BSDEs by studying them in a more general framework, with general driver, and to discuss comparison results for them. In a second step we are interested in partial differential equations (PDE) whose solutions can be stochastically interpreted in terms of Mean-Field BSDEs. For this we study a Mean-Field BSDE in a Markovian framework, associated with a Mean-Field forward equation. By combining classical BSDE methods, in particular that of ``backward semigroups" introduced by Peng [14], with specific arguments for Mean-Field BSDEs we prove that this Mean-Field BSDE describes the viscosity solution of a nonlocal PDE. The uniqueness of this viscosity solution is obtained for the space of continuous functions with polynomial growth. With the help of an example it is shown that for the nonlocal PDEs associated to Mean-Field BSDEs one cannot expect to have uniqueness in a larger space of continuous functions.
dc.descriptionThe results were presented by Rainer Buckdahn at the Mittag-Leffler Institute (Stockholm, Sweden) in November 8th, 2007. The paper was submitted
dc.identifierhttps://arxiv.org/abs/0711.2167
dc.identifierhttp://arxiv.org/abs/0711.2167
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/142475
dc.subjectProbability
dc.subjectSymplectic Geometry
dc.subject60H10; 60H30; 35K65
dc.titleMean-Field Backward Stochastic Differential Equations and Related Partial Differential Equations
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