Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 130, pp. 1-10.

Title: Newton's method for stochastic functional differential equations

Author: Monika Wrzosek (Univ. of Gdansk, Poland)

Abstract: 
 In this article, we apply Newton's method to stochastic functional 
 differential equations. The first part concerns a first-order convergence.
 We formulate a Gronwall-type inequality which plays an important role in
 the proof of the convergence theorem for the Newton method.
 In the second part a probabilistic second-order convergence is studied.

Submitted May 31, 2012. Published August 15, 2012.
Math Subject Classifications: 60H10, 60H35, 65C30.
Key Words: Newton's method; stochastic functional differential equations.