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.
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| Monika Wrzosek |
Institute of Mathematics, University of Gda\'nsk
Wita Stwosza 57, 80-952 Gda\'nsk, Poland
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