TY - JOUR

T1 - Wong–Zakai approximation of a stochastic partial differential equation with multiplicative noise

AU - Hausenblas, Erika

AU - Randrianasolo, Tsiry Avisoa

N1 - Publisher Copyright: © 2024 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.

PY - 2024/3/19

Y1 - 2024/3/19

N2 - In this article, we derive the convergence rate for the Wong–Zakai equation of some approximation of stochastic evolution equations with multiplicative noise. To be more precise, the diffusion coefficient in front of the noise is the multiplication operator, and, is therefore not bounded, a situation not treated in the literature. Since our motivation comes from problems in numerical ling, we consider a finite, high-dimensional problem approximating a stochastic evolution equation on a random time grid. By imposing suitable stability conditions on the drift term and the time grid, we achieve a convergence rate in the mean square of order (Formula presented.), for some (Formula presented.) and (Formula presented.).

AB - In this article, we derive the convergence rate for the Wong–Zakai equation of some approximation of stochastic evolution equations with multiplicative noise. To be more precise, the diffusion coefficient in front of the noise is the multiplication operator, and, is therefore not bounded, a situation not treated in the literature. Since our motivation comes from problems in numerical ling, we consider a finite, high-dimensional problem approximating a stochastic evolution equation on a random time grid. By imposing suitable stability conditions on the drift term and the time grid, we achieve a convergence rate in the mean square of order (Formula presented.), for some (Formula presented.) and (Formula presented.).

KW - 60J65

KW - 65C30

KW - multiplicative noise

KW - partial differential equations with randomness

KW - Primary 35R60

KW - Secondary 65M15

KW - Stochastic partial differential equations

KW - time-discretization scheme

KW - Wong–Zakai approximation

UR - http://www.scopus.com/inward/record.url?scp=85188542463&partnerID=8YFLogxK

UR - https://pureadmin.unileoben.ac.at/portal/en/publications/wongzakai-approximation-of-a-stochastic-partial-differential-equation-with-multiplicative-noise(7548d1b4-4ed9-4b59-9267-1b05b3fadf8f).html

U2 - 10.1080/00036811.2024.2331026

DO - 10.1080/00036811.2024.2331026

M3 - Article

VL - 2024

JO - Applicable Analysis

JF - Applicable Analysis

SN - 0003-6811

IS - ??? Stand: 15. April 2024

ER -