A Jump Ornstein-Uhlenbeck Bridge Based on Energy-optimal Control and Its Self-exciting Extension
Optimization and Control
2023-05-04 v5 Probability
Abstract
We study a version of the Ornstein-Uhlenbeck bridge driven by a spectrally-positive subordinator. Our formulation is based on a Linear-Quadratic control subject to a singular terminal condition. The Ornstein-Uhlenbeck bridge, we develop, is written as a limit of the obtained optimally controlled processes, and is shown to admit an explicit expression. Its extension with self-excitement is also considered. The terminal condition is confirmed to be satisfied by the obtained process both analytically and numerically. The methods are also applied to a streamflow regulation problem using a real-life dataset.
Keywords
Cite
@article{arxiv.2302.10345,
title = {A Jump Ornstein-Uhlenbeck Bridge Based on Energy-optimal Control and Its Self-exciting Extension},
author = {Hidekazu Yoshioka and Kazutoshi Yamazaki},
journal= {arXiv preprint arXiv:2302.10345},
year = {2023}
}
Comments
This is a preprint version of the article with the same title to be published in "IEEE Control Systems Letters" (L-CSS)