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Newton’s method for first-order stochastic functional partial differential equations

Monika Wrzosek — 2014

Commentationes Mathematicae

We apply Newton’s method to hyperbolic stochastic functional partial differential equations of the first order driven by a multidimensional Brownian motion. We prove a first-order convergence and a second-order convergence in a probabilistic sense.

The method of lines for hyperbolic stochastic functional partial differential equations

Monika Wrzosek; Maria Ziemlańska — 2018

Czechoslovak Mathematical Journal

We apply an approximation by means of the method of lines for hyperbolic stochastic functional partial differential equations driven by one-dimensional Brownian motion. We study the stability with respect to small $L^{2}$ -perturbations.

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