Electron. J. Differential Equations, Vol. 2021 (2021), No. 98, pp. 1-16.

Newton-Kantorovitch method for decoupled forward-backward stochastic differential equations

Dai Taguchi, Takahiro Tsuchiya

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.

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Dai Taguchi
Research Institute for Interdisciplinary Science
Okayama University 3-1-1 Tsushima-naka
Kita-ku Okayama 700-8530, Japan
email: dai.taguchi.dai@gmail.com
Takahiro Tsuchiya
School of Computer Science and Engineering
The University of Aizu, Japan
email: suci@probab.com

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