The conditioned Lyapunov spectrum for random dynamical systems
Dynamical Systems
2025-08-21 v2 Probability
Abstract
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 -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.
Cite
@article{arxiv.2204.04129,
title = {The conditioned Lyapunov spectrum for random dynamical systems},
author = {Matheus M. Castro and Dennis Chemnitz and Hugo Chu and Maximilian Engel and Jeroen S. W. Lamb and Martin Rasmussen},
journal= {arXiv preprint arXiv:2204.04129},
year = {2025}
}
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34 pages, 0 figures