Functional limit theorems for a time-changed multidimensional Wiener process
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916571850473472 |
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| author | Mishura, Yuliia Schilling, René L. |
| author_facet | Mishura, Yuliia Schilling, René L. |
| contents | We study the asymptotic behaviour of a properly normalized time-changed multidimensional Wiener process; the time change is given by an additive functional of the Wiener process itself. At the level of generators, the time change means that we consider the Laplace operator -- which generates a multidimensional Wiener process -- and multiply it by a (possibly degenerate) state-space dependent intensity. We assume that the intensity admits limits at infinity in each octant of the state space, but the values of these limits may be different. Applying a functional limit theorem for the superposition of stochastic processes, we prove functional limit theorems for the normalized time-changed multidimensional Wiener process. Among the possible limits there is a multidimensional analogue of skew Brownian motion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_10820 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Functional limit theorems for a time-changed multidimensional Wiener process Mishura, Yuliia Schilling, René L. Probability 60J65, 60J60, 60J55, 60F05, 60F17 We study the asymptotic behaviour of a properly normalized time-changed multidimensional Wiener process; the time change is given by an additive functional of the Wiener process itself. At the level of generators, the time change means that we consider the Laplace operator -- which generates a multidimensional Wiener process -- and multiply it by a (possibly degenerate) state-space dependent intensity. We assume that the intensity admits limits at infinity in each octant of the state space, but the values of these limits may be different. Applying a functional limit theorem for the superposition of stochastic processes, we prove functional limit theorems for the normalized time-changed multidimensional Wiener process. Among the possible limits there is a multidimensional analogue of skew Brownian motion. |
| title | Functional limit theorems for a time-changed multidimensional Wiener process |
| topic | Probability 60J65, 60J60, 60J55, 60F05, 60F17 |
| url | https://arxiv.org/abs/2501.10820 |