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MEAN-FIELD BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS: A LIMIT APPROACH
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.ORCID-id: 0000-0002-6608-0715
2009 (engelsk)Inngår i: Annals of Probability, ISSN 0091-1798, E-ISSN 2168-894X, Vol. 37, nr 4, s. 1524-1565Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

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 (X-N, Y-N, Z(N)) of some decoupled forward-backward equation which coefficients are governed by N independent copies of (X-N, Y-N, Z(N)). We show that the convergence speed of this approximation is of order 1/root N. Moreover, our special choice of the approximation allows to characterize the limit behavior of root N(X-N - X, Y-N - Y, Z(N) - 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.

sted, utgiver, år, opplag, sider
2009. Vol. 37, nr 4, s. 1524-1565
Emneord [en]
Backward stochastic differential equation, mean-field approach, McKean-Vlasov equation, mean-field BSDE, tightness, weak convergence, mckean-vlasov, particle method
Identifikatorer
URN: urn:nbn:se:kth:diva-18662DOI: 10.1214/08-aop442ISI: 000268692700010Scopus ID: 2-s2.0-69249229620OAI: oai:DiVA.org:kth-18662DiVA, id: diva2:336709
Merknad
QC 20100525Tilgjengelig fra: 2010-08-05 Laget: 2010-08-05 Sist oppdatert: 2017-12-12bibliografisk kontrollert

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