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From Particle Systems to Partial Differential Equations III pp 99–120Cite as

Asymptotics for FBSDES with Jumps and Connections with Partial Integral Differential Equations

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 162))

Abstract

It is our intention to survey the asymptotic study of a certain class of coupled forward-backward stochastic differential equations (FBSDEs for short) when the noise terms in the forward diffusion have small intensities that converge to zero. The system of FBSDEs discussed can be used to give a probabilistic representation for the solution in the viscosity sense of an associated system of partial-integral differential equations (PIDEs) with a terminal condition. The asymptotic study of this PIDE is done probabilistically using the FBSDE system. Secondly we present a large deviations principle for the laws of the forward and backward processes of the stochastic system.

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Acknowledgments

The author would like to thank the editors and the anonymous reviewers for their comments, suggestions and several corrections. The author acknowledges the financial support by the project IRTG 1740/ TRP 2011/50151-0 funded by the DFG/FAPESP.

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Authors and Affiliations

  1. Instititut für Mathematik, Humboldt-Universität zu Berlin, Rudower Chaussee 25 - Johann von Neumann Haus, 12489, Berlin, Germany

    André de Oliveira Gomes

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  1. André de Oliveira Gomes
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Correspondence to André de Oliveira Gomes .

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Editors and Affiliations

  1. University of Minho Department of Mathematics, Braga, Portugal

    Patrícia Gonçalves

  2. University of Minho Department of Mathematics, Braga, Portugal

    Ana Jacinta Soares

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de Oliveira Gomes, A. (2016). Asymptotics for FBSDES with Jumps and Connections with Partial Integral Differential Equations. In: Gonçalves, P., Soares, A. (eds) From Particle Systems to Partial Differential Equations III. Springer Proceedings in Mathematics & Statistics, vol 162. Springer, Cham. https://doi.org/10.1007/978-3-319-32144-8_5

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