Path-dependent Poisson random measures and stochastic integrals constructed from general point processes

Konatsu Miyamoto

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arXiv · 2109.04578

Path-dependent Poisson random measures and stochastic integrals constructed from general point processes

Konatsu Miyamoto

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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.

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Konatsu Miyamoto. 2021-09-09. Path-dependent Poisson random measures and stochastic integrals constructed from general point processes. https://arxiv.org/abs/2109.04578

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