確率論セミナー


2018/5/22(Tue)

16:30--18:00 数学教室 大セミナー室 (E404)

田口 大

大阪大学基礎工学研究科

Newton's method for BSDEs

It is well known that Newton's method is a linear approximation method to find a real roof of non-linear equations. Newton (1669) introduced the method to find a real root of third degree equations. Kantorivitch (1948) extended Newton's method to non-linear equations on Banach space by using Frechet derivative. Chaplygin (1954) introduced a linear approximation for a solution of initial value problem on (non-linear) ordinary differential equation, and Visossich (1978) proved that Chaplygin's method is equivalent to Newton's method for some integral operator. Kawabata and Yamada (1991) introduced Newton's method for stochastic differential equation by using Gateaux derivative for some stochastic integral operator, and Ouknine(1993) and Amano(2009) provided its rate of convergence. The aim of this talk is to formulate Newton's method for decoupled forward-backward stochastic differential equations (FBSDEs). We will show that Newton's approximation is well-defined and satisfies a linear FBSDE, and we will provide its rate of convergence. This talk is based on joint work with Takahiro Tsuchiya (The University of Aizu).