TY - JOUR
T1 - Strong solutions of forward–backward stochastic differential equations with measurable coefficients
AU - Luo, Peng
AU - Menoukeu-Pamen, Olivier
AU - Tangpi, Ludovic
N1 - Funding Information:
Financial support from the National Natural Science Foundation of China (Grant No. 12101400) is gratefully acknowledged.Financial support from the Alexander von Humboldt Foundation, Germany, under the program financed by the German Federal Ministry of Education and Research entitled German Research Chair No 01DG15010 is gratefully acknowledged.Financial support by NSF, United States grant DMS-2005832 is gratefully acknowledged.
Publisher Copyright:
© 2021 Elsevier B.V.
PY - 2022/2
Y1 - 2022/2
N2 - This paper investigates solvability of fully coupled systems of forward–backward stochastic differential equations (FBSDEs) with irregular coefficients. In particular, we assume that the coefficients of the FBSDEs are merely measurable and bounded in the forward process. We crucially use compactness results from the theory of Malliavin calculus to construct strong solutions. Despite the irregularity of the coefficients, the solutions turn out to be differentiable, at least in the Malliavin sense and, as functions of the initial variable, in the Sobolev sense.
AB - This paper investigates solvability of fully coupled systems of forward–backward stochastic differential equations (FBSDEs) with irregular coefficients. In particular, we assume that the coefficients of the FBSDEs are merely measurable and bounded in the forward process. We crucially use compactness results from the theory of Malliavin calculus to construct strong solutions. Despite the irregularity of the coefficients, the solutions turn out to be differentiable, at least in the Malliavin sense and, as functions of the initial variable, in the Sobolev sense.
KW - FBSDE
KW - Malliavin calculus
KW - Singular PDEs
KW - Singular coefficients
KW - Sobolev regularity
KW - Strong solutions
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U2 - 10.1016/j.spa.2021.10.012
DO - 10.1016/j.spa.2021.10.012
M3 - Article
AN - SCOPUS:85119298619
SN - 0304-4149
VL - 144
SP - 1
EP - 22
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
ER -