Electronic Communications in Probability

Discrete maximal regularity of an implicit Euler–Maruyama scheme with non-uniform time discretisation for a class of stochastic partial differential equations

Yoshihito Kazashi

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Abstract

An implicit Euler–Maruyama method with non-uniform step-size applied to a class of stochastic partial differential equations is studied. A spectral method is used for the spatial discretization and the truncation of the Wiener process. A discrete analogue of maximal $L^2$-regularity of the scheme and the discretised stochastic convolution is established, which has the same form as their continuous counterpart.

Article information

Source
Electron. Commun. Probab., Volume 23 (2018), paper no. 29, 14 pp.

Dates
Received: 20 October 2017
Accepted: 4 April 2018
First available in Project Euclid: 28 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1524881137

Digital Object Identifier
doi:10.1214/18-ECP130

Mathematical Reviews number (MathSciNet)
MR3798240

Zentralblatt MATH identifier
1390.60236

Subjects
Primary: 60H15: Stochastic partial differential equations [See also 35R60] 60H35: Computational methods for stochastic equations [See also 65C30]

Keywords
multiplicative noise non-uniform time discretisation implicit Euler–Maruyama scheme

Rights
Creative Commons Attribution 4.0 International License.

Citation

Kazashi, Yoshihito. Discrete maximal regularity of an implicit Euler–Maruyama scheme with non-uniform time discretisation for a class of stochastic partial differential equations. Electron. Commun. Probab. 23 (2018), paper no. 29, 14 pp. doi:10.1214/18-ECP130. https://projecteuclid.org/euclid.ecp/1524881137


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