PreprintarXiv licencearXiv
Further Approaches of Dynamical Low-Rank Approximation for SDEs
Abstract
In this article, we propose two other DLRA-type dynamics for stochastic differential equations (SDEs) than the one studied in arXiv:2308.11581, derived from a minimization of functionals and (informally) from a Stratonovich formulation, respectively. The former approach resembles the DLRA for SDE system proposed in arXiv:1803.00499. Providing the differentiability of the diffusion, the latter procedure registers an additional term in the drift. Indeed, its derivation exploits the Stratonovich formulation to write stochastic processes on manifold, and, hence, possesses a term that depends on the geometry of the manifold itself. These developments open the debate on which formalism is more suitable and what DLRA for SDEs really is.
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BibTeX
@misc{kazashi2026further,
title = {{Further Approaches of Dynamical Low-Rank Approximation for SDEs}},
author = {Yoshihito Kazashi and Fabio Nobile and Fabio Zoccolan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20292},
eprint = {2609.20292},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20292},
}
RIS
TY - UNPB
TI - Further Approaches of Dynamical Low-Rank Approximation for SDEs
AU - Yoshihito Kazashi
AU - Fabio Nobile
AU - Fabio Zoccolan
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.20292
UR - https://arxiv.org/abs/2609.20292
AB - In this article, we propose two other DLRA-type dynamics for stochastic differential equations (SDEs) than the one studied in arXiv:2308.11581, derived from a minimization of functionals and (informally) from a Stratonovich formulation, respectively. The former approach resembles the DLRA for SDE system proposed in arXiv:1803.00499. Providing the differentiability of the diffusion, the latter procedure registers an additional term in the drift. Indeed, its derivation exploits the Stratonovich formulation to write stochastic processes on manifold, and, hence, possesses a term that depends on the geometry of the manifold itself. These developments open the debate on which formalism is more suitable and what DLRA for SDEs really is.
ER -