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An efficient data-driven approximation to the stochastic differential equations with non-global Lipschitz coefficient and multiplicative noise
- Source :
- AIMS Mathematics, Vol 9, Iss 5, Pp 11975-11991 (2024)
- Publication Year :
- 2024
- Publisher :
- AIMS Press, 2024.
-
Abstract
- This paper studied the numerical approximation of the stochastic differential equations driven by non-global Lipschitz drift coefficient and multiplicative noise. An efficient data-driven method, called extended continuous latent process flow, was proposed for the underlying problem. Compared with the piecewise construction of a variational posterior process used in the classical continuous latent process flow developed by Deng et al. [13], the principle idea of our method was to derive a variational lower bound by constructing a posterior latent process conditional on all information over the whole time interval to maximize the log-likelihood generated by the observations, which reduces the computational cost and, thus, provides a convenient way to approximate the considered equation. Particularly, our new method showed a better approximation to the underlying equation than the classical drift-$ \theta $ discretization scheme through numerical error comparison. Numerical experiments were finally reported to demonstrate the effectiveness and generalization performance of the proposed method.
Details
- Language :
- English
- ISSN :
- 24736988
- Volume :
- 9
- Issue :
- 5
- Database :
- Directory of Open Access Journals
- Journal :
- AIMS Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.f271bcab27684691a6dbbf096f9a7de6
- Document Type :
- article
- Full Text :
- https://doi.org/10.3934/math.2024585?viewType=HTML