English

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 QQ-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.

Keywords

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}
}

Comments

34 pages, 0 figures

R2 v1 2026-06-24T10:42:34.920Z