Weak solutions for forward--backward SDEs--a martingale problem approach

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dc.creatorMa, Jin
dc.creatorZhang, Jianfeng
dc.creatorZheng, Ziyu
dc.date2009-01-19
dc.date.accessioned2026-07-07T12:31:35Z
dc.date.available2026-07-07T12:31:35Z
dc.descriptionIn this paper, we propose a new notion of Forward--Backward Martingale Problem (FBMP), and study its relationship with the weak solution to the forward--backward stochastic differential equations (FBSDEs). The FBMP extends the idea of the well-known (forward) martingale problem of Stroock and Varadhan, but it is structured specifically to fit the nature of an FBSDE. We first prove a general sufficient condition for the existence of the solution to the FBMP. In the Markovian case with uniformly continuous coefficients, we show that the weak solution to the FBSDE (or equivalently, the solution to the FBMP) does exist. Moreover, we prove that the uniqueness of the FBMP (whence the uniqueness of the weak solution) is determined by the uniqueness of the viscosity solution of the corresponding quasilinear PDE.
dc.descriptionPublished in at http://dx.doi.org/10.1214/08-AOP0383 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/0901.2790
dc.identifierhttp://arxiv.org/abs/0901.2790
dc.identifierAnnals of Probability 2008, Vol. 36, No. 6, 2092-2125
dc.identifierdoi:10.1214/08-AOP0383
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/216491
dc.subjectProbability
dc.subject60H10 (Primary), 35K55, 60H30 (Secondary)
dc.titleWeak solutions for forward--backward SDEs--a martingale problem approach
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