Harmonic problems arising from continuous time random walks limit processes
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916746679549952 |
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| author | Biočić, Ivan Toaldo, Bruno |
| author_facet | Biočić, Ivan Toaldo, Bruno |
| contents | In this paper, we develop a universal method that identifies the (non-local) governing evolution equations for Continuous Time Random Walks' (CTRWs) limit processes. Given one of these processes, our method provides the form of a non-local operator, acting on space and time variables jointly, such that the (generalized) harmonic problem associated with it represents an evolution governing equation for this process. Then, the well-posedness of this problem must be established case by case. In this paper, we establish well-posedness when the process is a Feller process (on a general Polish space $E$) time-changed with the overshooting of a subordinator. Also, we will show how our method applies to several cases when the equation and its well-posedness are already known, hence unifying several different approaches in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_14550 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Harmonic problems arising from continuous time random walks limit processes Biočić, Ivan Toaldo, Bruno Probability 60K50, 60K15, 35R11, 31C05 In this paper, we develop a universal method that identifies the (non-local) governing evolution equations for Continuous Time Random Walks' (CTRWs) limit processes. Given one of these processes, our method provides the form of a non-local operator, acting on space and time variables jointly, such that the (generalized) harmonic problem associated with it represents an evolution governing equation for this process. Then, the well-posedness of this problem must be established case by case. In this paper, we establish well-posedness when the process is a Feller process (on a general Polish space $E$) time-changed with the overshooting of a subordinator. Also, we will show how our method applies to several cases when the equation and its well-posedness are already known, hence unifying several different approaches in the literature. |
| title | Harmonic problems arising from continuous time random walks limit processes |
| topic | Probability 60K50, 60K15, 35R11, 31C05 |
| url | https://arxiv.org/abs/2505.14550 |