Continuity Results and Estimates for the Lyapunov Exponent of Brownian Motion in Random Potential

2014/04/04 by Johannes Rueß, Rueß, Johannes
Economics, Econometrics and Finance · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1404.1273

openalex publication_date 2014/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We collect some applications of the variational formula established by Schröder (1988) and Rueß(2013) for the quenched Lyapunov exponent of Brownian motion in stationary and ergodic nonnegative potential. We show for example that the Lyapunov exponent for nondeterministic potential is strictly lower than the Lyapunov exponent for the averaged potential. The behaviour of the Lyapunov exponent under independent perturbations of the underlying potential is examined. And with the help of counterexamples we are able to give a detailed picture of the continuity properties of the Lyapunov exponent.

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