Geodesic
Newton's method for stochastic functional differential equations
Electronic journal of differential equations, Tome 2012 (2012)
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.
Classification : 60H10, 60H35, 65C30
Keywords: Newton's method, stochastic functional differential equations 
@article{EJDE_2012__2012__a85,
     author = {Wrzosek,  Monika},
     title = {Newton's method for stochastic functional differential equations},
     journal = {Electronic journal of differential equations},
     year = {2012},
     volume = {2012},
     zbl = {1254.60075},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a85/}
}
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%J Electronic journal of differential equations
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Wrzosek,  Monika. Newton's method for stochastic functional differential equations. Electronic journal of differential equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a85/