Gaussian density estimates for solutions of fully coupled forward‐backward SDEs

We obtain upper and lower Gaussian density estimates for the laws of each component of the solution to a one‐dimensional fully coupled forward‐backward SDE. Our approach relies on the link between FBSDEs and quasilinear parabolic PDEs, and is fully based on the use of classical results on PDEs rathe...

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Bibliographic Details
Published in:Mathematische Nachrichten 2020-08, Vol.293 (8), p.1554-1564
Main Authors: Olivera, Christian, Shamarova, Evelina
Format: Article
Language:English
Subjects:
Density
density estimates
forward‐backward SDEs
Malliavin calculus
Nourdin–Viens' formula
Parabolic differential equations
Partial differential equations
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Summary:We obtain upper and lower Gaussian density estimates for the laws of each component of the solution to a one‐dimensional fully coupled forward‐backward SDE. Our approach relies on the link between FBSDEs and quasilinear parabolic PDEs, and is fully based on the use of classical results on PDEs rather than on manipulation of FBSDEs, compared to other papers on this topic. This essentially simplifies the analysis.
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.201800381