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August 2016 Continuity results and estimates for the Lyapunov exponent of Brownian motion in stationary potential
Johannes Rueß
Braz. J. Probab. Stat. 30(3): 435-463 (August 2016). DOI: 10.1214/15-BJPS288

Abstract

We collect some applications of the variational formula established by Schroeder [J. Funct. Anal. 77 (1988) 60–87] and Rueß [ALEA Lat. Am. J. Probab. Math. Stat. 11 (2014) 679–709] 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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Johannes Rueß. "Continuity results and estimates for the Lyapunov exponent of Brownian motion in stationary potential." Braz. J. Probab. Stat. 30 (3) 435 - 463, August 2016. https://doi.org/10.1214/15-BJPS288

Information

Received: 1 May 2014; Accepted: 1 March 2015; Published: August 2016
First available in Project Euclid: 29 July 2016

zbMATH: 1370.37105
MathSciNet: MR3531693
Digital Object Identifier: 10.1214/15-BJPS288

Rights: Copyright © 2016 Brazilian Statistical Association

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Vol.30 • No. 3 • August 2016
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