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Forward and Backward Stochastic Differential Equations with normal constraint in law

Briand, Philippe; Cardaliaguet, Pierre; Chaudru de Raynal, Paul-Eric; Hu, Ying (2020), Forward and Backward Stochastic Differential Equations with normal constraint in law, Stochastic Processes and their Applications, 130, 12, p. 7021-7097. 10.1016/j.spa.2020.07.007

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SEwNMR_PREPRINT_20190228.pdf (789.8Kb)
Type
Article accepté pour publication ou publié
Date
2020
Journal name
Stochastic Processes and their Applications
Volume
130
Number
12
Publisher
Elsevier
Pages
7021-7097
Publication identifier
10.1016/j.spa.2020.07.007
Metadata
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Author(s)
Briand, Philippe
Laboratoire de Mathématiques [LAMA]
Cardaliaguet, Pierre
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Chaudru de Raynal, Paul-Eric
Laboratoire de Mathématiques [LAMA]
Hu, Ying
Institut de Recherche Mathématique de Rennes [IRMAR]
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.
Subjects / Keywords
stochastic differential equations; Wasserstein space

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