Wong–Zakai approximation of a stochastic partial differential equation with multiplicative noise
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In: Applicable Analysis, Vol. 103.2024, No. 16, 19.03.2024, p. 3029-3048.
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TY - JOUR
T1 - Wong–Zakai approximation of a stochastic partial differential equation with multiplicative noise
AU - Hausenblas, Erika
AU - Randrianasolo, Tsiry
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 min{1−𝛿,2−2𝛾}, for some 0<𝛿<1 and 0<𝛾<1/2.
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 min{1−𝛿,2−2𝛾}, for some 0<𝛿<1 and 0<𝛾<1/2.
KW - multiplicative noise
KW - partial differential equations with randomness
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 - 103.2024
SP - 3029
EP - 3048
JO - Applicable Analysis
JF - Applicable Analysis
SN - 0003-6811
IS - 16
ER -
