The conditioned Lyapunov spectrum for random dynamical systems

2022/04/08 by Matheus M. Castro, Dennis Chemnitz, Castro, Matheus M. +9 · 1 citation
Biochemistry, Genetics and Molecular Biology · Engineering · #37H05 #37H15 #47D07 #60J05 #60J25 #Dynamical Systems (math.DS) #FOS: Mathematics #Gene Regulatory Network Analysis #Probability (math.PR) #Receptor Mechanisms and Signaling #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2204.04129

openalex publication_date 2022/04/08 · openalex created_date 2023/02/12 · openalex updated_date 2026/07/28

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.

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• Conditioned stochastic stability of equilibrium states on uniformly hyperbolic sets

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