Path-dependent Poisson random measures and stochastic integrals constructed from general point processes
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866914932416577536 |
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| author | Miyamoto, Konatsu |
| author_facet | Miyamoto, Konatsu |
| contents | 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 Itô's formula. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_04578 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Path-dependent Poisson random measures and stochastic integrals constructed from general point processes Miyamoto, Konatsu Probability 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 Itô's formula. |
| title | Path-dependent Poisson random measures and stochastic integrals constructed from general point processes |
| topic | Probability |
| url | https://arxiv.org/abs/2109.04578 |