The conditioned Lyapunov spectrum for random dynamical systems
- Authors: Matheus M. Castro, Dennis Chemnitz, Hugo Chu, Maximilian Engel, Jeroen S. W. Lamb, Martin Rasmussen
- Preprint year: 2022
- First public date: 2022-04-08
- arXiv: 2204.04129
- Status: Published
- Publication type: Journal article
- Publication year: 2025
- Journal: Annales de l’Institut Henri Poincaré B 61(3), 1845–1877 (2025)
- DOI: 10.1214/24-AIHP1466
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 $Q$-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.