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Newton-Kantorovitch method for decoupled forward-backward stochastic differential equations (1806.01493v1)
Published 5 Jun 2018 in math.PR and math.NA
Abstract: We present and prove a Newton-Kantorovitch method for solving decoupled forward-backward stochastic differential equations (FBSDEs) involving smooth coefficients with uniformly bounded derivatives. As Newton's method is required a suitable initial condition to converge, we show that such initial conditions are solutions of a linear backward stochastic differential equation. In addition, we show that converges linearly to the solution.
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