Wong–Zakai approximation of a stochastic partial differential equation with multiplicative noise
Research output: Contribution to journal › Article › Research › peer-review
Authors
Organisational units
Abstract
Abstract
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.
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.
Details
Original language | English |
---|---|
Number of pages | 19 |
Journal | Applicable Analysis |
Volume | 2024 |
Issue number | 103 |
DOIs | |
Publication status | Published - 19 Mar 2024 |