Path-dependent Poisson random measures and stochastic integrals constructed from general point processes
Probability
2024-09-04 v2
Abstract
In this paper, we consider an extension of the Poisson random measure for the formulation of continuous-time reinforcement learning, such that both the frequency and the width of the jumps depend on the path. Starting from a general point process, we define a new Poisson random measure as limit of the linear sum of these counting processes, and name it the Mesgaki random measure. We also construct its Stochastic integral and It\^o's formula.
Cite
@article{arxiv.2109.04578,
title = {Path-dependent Poisson random measures and stochastic integrals constructed from general point processes},
author = {Konatsu Miyamoto},
journal= {arXiv preprint arXiv:2109.04578},
year = {2024}
}
Comments
It was clearly too playful in the way the words were chosen. arXiv admin note: the author affiliation in the paper is incorrect