Electronic Journal of Differential Equations, Vol. 2021 (2021), No. 98, pp. 1-16.

Title: Newton-Kantorovitch method for decoupled forward-backward stochastic
differential equations
       
Authors: Dai Taguchi (Okayama Univ. Kita-ku Okayama, Japan)
         Takahiro Tsuchiya (Univ. of Aizu, Japan)

Abstract:
We formulate a Newton-Kantorovitch method for solving decoupled forward-backward
stochastic differential equations involving smooth and degenerate coefficients with
uniformly bounded derivatives. We show that it converges globally and
its rate of convergence is exponential.

Submitted January 19, 2021. Published December 20, 2021.
Math Subject Classifications: 49M15, 65C30, 41A25, 60H35, 41A25, 60H10.
Key Words: Stochastic differential equation; Newton-type methods; rate of convergence.