Kawabata and Yamada  proposed an implicit Newton method for stochastic differential equations and proved its convergence. They proved an error estimate in a sufficiently small time interval and extended it to a global convergence theorem by using open-closed method. In this note, the author gives an explicit Newton scheme which is equivalent to Kawabata-Yamada’s implicit formulation (Remark 1) and prove its direct error estimate (Theorem 2.1). His result could provide a key to solve the open problem of second order convergence (see Remark of Theorem 2.1 and ).
"A note on Newton’s method for stochastic differential equations and its error estimate." Proc. Japan Acad. Ser. A Math. Sci. 85 (3) 19 - 21, March 2009. https://doi.org/10.3792/pjaa.85.19