Newton’s method for nonlinear stochastic wave equations

Henryk Leszczyński , Monika Wrzosek

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.
Author Henryk Leszczyński (FMPI/IM)
Henryk Leszczyński,,
- Institute of Mathematics
, Monika Wrzosek (FMPI/IM)
Monika Wrzosek,,
- Institute of Mathematics
Journal seriesForum Mathematicum, ISSN 0933-7741, e-ISSN 1435-5337, (N/A 100 pkt)
Issue year2020
Vol32
No3
Pages595-605
Publication size in sheets0.50
Keywords in EnglishNewton’s method, wave equation, probabilistic convergence, nonlocal dependence, Cairoli’s maximal inequality
ASJC Classification2600 General Mathematics; 2604 Applied Mathematics
DOIDOI:10.1515/forum-2019-0090
Languageen angielski
Score (nominal)100
Score sourcejournalList
ScoreMinisterial score = 100.0, 27-07-2020, ArticleFromJournal
Publication indicators WoS Citations = 0.000; Scopus SNIP (Source Normalised Impact per Paper): 2019 = 1.084; WoS Impact Factor: 2018 = 0.867 (2) - 2018=0.743 (5)
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