The conditioned Lyapunov spectrum for random dynamical systems
Fuente:
arXiv
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| Autores principales: | , , , , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911111678263296 |
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| author | Castro, Matheus M. Chemnitz, Dennis Chu, Hugo Engel, Maximilian Lamb, Jeroen S. W. Rasmussen, Martin |
| author_facet | Castro, Matheus M. Chemnitz, Dennis Chu, Hugo Engel, Maximilian Lamb, Jeroen S. W. Rasmussen, Martin |
| contents | We establish the existence of a full spectrum of Lyapunov exponents for memoryless random dynamical systems with absorption. To this end, we crucially embed the process conditioned to never being absorbed, the $Q$-process, into the framework of random dynamical systems, allowing us to study multiplicative ergodic properties. We show that the finite-time Lyapunov exponents converge in conditioned probability and apply our results to iterated function systems and stochastic differential equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_04129 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The conditioned Lyapunov spectrum for random dynamical systems Castro, Matheus M. Chemnitz, Dennis Chu, Hugo Engel, Maximilian Lamb, Jeroen S. W. Rasmussen, Martin Dynamical Systems Probability 37H05, 37H15, 47D07, 60J05, 60J25 We establish the existence of a full spectrum of Lyapunov exponents for memoryless random dynamical systems with absorption. To this end, we crucially embed the process conditioned to never being absorbed, the $Q$-process, into the framework of random dynamical systems, allowing us to study multiplicative ergodic properties. We show that the finite-time Lyapunov exponents converge in conditioned probability and apply our results to iterated function systems and stochastic differential equations. |
| title | The conditioned Lyapunov spectrum for random dynamical systems |
| topic | Dynamical Systems Probability 37H05, 37H15, 47D07, 60J05, 60J25 |
| url | https://arxiv.org/abs/2204.04129 |