The Lyapunov spectrum for conditioned random dynamical systems
@inproceedings{Castro2022TheLS,
title={The Lyapunov spectrum for conditioned random dynamical systems},
author={Matheus M. Castro and Dennis Chemnitz and Hugo Chu and Maximilian Engel and Jeroen S.W. Lamb and Martin Rasmussen},
year={2022}
}. 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.
One Citation
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