A note on Newton's method for stochastic differential equations and its error estimate (Q1030572)

The author gives an explicite Newton scheme for stochastic differential equations which is equivalent to Kawabata-Yamada's implicite formulation. The direct error estimate for this scheme is proven that is a bound for the supremum of the second moment of the estimate on a interval is given. This result gives a simple proof of Kawabata and Yamada's convergence theorem. The author suggests that his result could provide a key to solve the open problem of the second order convergence.