Mean-field backward stochastic differential equations: A limit approach

Rainer Buckdahn, Boualem Djehiche, Juan Li, Shige Peng

Research output: Contribution to journalArticlepeer-review


Mathematical mean-field approaches play an important role in different fields of Physics and Chemistry, but have found in recent works also their application in Economics, Finance and Game Theory. The objective of our paper is to investigate a special mean-field problem in a purely stochastic approach: for the solution (Y,Z) of a mean-field backward stochastic differential equation driven by a forward stochastic differential of McKean-Vlasov type with solution X we study a special approximation by the solution (XN,YN,ZN) of some decoupled forward-backward equation which coefficients are governed by N independent copies of (XN,YN,ZN). We show that the convergence speed of this approximation is of order 1/√N. Moreover, our special choice of the approximation allows to characterize the limit behavior of √N(XN -X, YN -Y,ZN -Z). We prove that this triplet converges in law to the solution of some forward-backward stochastic differential equation of mean-field type, which is not only governed by a Brownian motion but also by an independent Gaussian field.

Original languageEnglish (US)
Pages (from-to)1524-1565
Number of pages42
JournalAnnals of Probability
Issue number4
StatePublished - Jul 2009


  • Backward stochastic differential equation
  • McKean-Vlasov equation
  • Mean-field approach
  • Mean-field BSDE
  • Tightness
  • Weak convergence

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


Dive into the research topics of 'Mean-field backward stochastic differential equations: A limit approach'. Together they form a unique fingerprint.

Cite this