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ETNA - Electronic Transactions on Numerical Analysis
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |
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DATUM, UNTERSCHRIFT / DATE, SIGNATURE
BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
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ETNA - Electronic Transactions on Numerical Analysis, pp. 77-87, 2020/02/04
We perform a time-space discretisation, known as the leap-frog method, for nonlinear stochastic functionalwave equations driven by multiplicative time-space white noise. To prove its stability weapply Cairoli's maximal inequalitiesfor two-parameter martingales and provide a lemma for estimating solutions to a class ofstochastic wave equations and a Gronwall-typeinequality over cones. The method converges in $L^2$ at a rate of $O(\\sqrt{h})$, where $h$is a time-space step size.
Keywords: leap-frog, stochastic wave equation