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Licensed Unlicensed Requires Authentication Published by De Gruyter February 11, 2020

Newton’s method for nonlinear stochastic wave equations

  • Henryk Leszczyński and Monika Wrzosek EMAIL logo
From the journal Forum Mathematicum

Abstract

We consider nonlinear stochastic wave equations driven by time-space white noise. The existence of solutions is proved by the method of successive approximations. Next we apply Newton’s method. The main result concerning its first-order convergence is based on Cairoli’s maximal inequalities for two-parameter martingales. Moreover, a second-order convergence in a probabilistic sense is demonstrated.

MSC 2010: 60H15; 35R60; 35R10

Communicated by Maria Gordina


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Received: 2019-04-05
Revised: 2019-09-18
Published Online: 2020-02-11
Published in Print: 2020-05-01

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