# A Jump Ornstein-Uhlenbeck Bridge Based on Energy-optimal Control and Its Self-exciting Extension

arXiv: https://arxiv.org/abs/2302.10345 · HTML: https://mlsanity.com/paper/2302.10345/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Feb 2023.

## Built on by (most cited first, 1 of 1)

- [Orlicz regrets to consistently bound statistics of random variables with an application to environmental indicators](https://mlsanity.com/paper/2310.05168/) (2023)

## Abstract (arXiv)

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.