A Note On Newton'S Method For System Of Stochastic Differential Equations

Kawabata and Yamada (1991) proposed an implicit formulation for Newton's method for an univariate stochastic differential equation (SDEs). Amano (2009) used the linearized equation technique and proposed explicit formulation for the Newton scheme. In this note, we extend the Newton method for univariate SDEs to the multivariate cases. The error analysis is given and some examples are proposed. Results show that the method works well.