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Forward and Backward Stochastic Differential Equations with normal constraint in law

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SEwNMR_PREPRINT_20190228.pdf (789.8Kb)
Date
2019
Publisher city
Paris
Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Publishing date
03-2019
Collection title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Link to item file
https://hal.archives-ouvertes.fr/hal-02053777
Dewey
Probabilités et mathématiques appliquées
Sujet
stochastic differential equations; Wasserstein space
URI
https://basepub.dauphine.fr/handle/123456789/18575
Collections
  • CEREMADE : Publications
Metadata
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Author
Briand, Philippe
79 Laboratoire de Mathématiques [LAMA]
Cardaliaguet, Pierre
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Chaudru de Raynal, Paul-Éric
79 Laboratoire de Mathématiques [LAMA]
Hu, Ying
75 Institut de Recherche Mathématique de Rennes [IRMAR]
Type
Document de travail / Working paper
Item number of pages
67
Abstract (EN)
In this paper we investigate the well-posedness of backward or forward stochastic differential equations whose law is constrained to live in an a priori given (smooth enough) set and which is reflected along the corresponding "normal" vector. We also study the associated interacting particle system reflected in mean field and asymptotically described by such equations. The case of particles submitted to a common noise as well as the asymptotic system is studied in the forward case. Eventually, we connect the forward and backward stochastic differential equations with normal constraints in law with partial differential equations stated on the Wasserstein space and involving a Neumann condition in the forward case and an obstacle in the backward one.

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