Asymptotic behaviour of time averages for non-ergodic Gaussian processes

作者：Slezak Jakub^*

来源：Annals of Physics, 2017, 383: 285-311.

DOI：10.1016/j.aop.2017.05.015

• Ergodicity breaking
• Gaussian process
• Statistical analysis
• Generalised Langevin equation

In this work, we study the behaviour of time-averages for stationary (non-ageing), but ergodicity-breaking Gaussian processes using their representation in Fourier space. We provide explicit formulae for various time-averaged quantities, such as mean square displacement, density, and analyse the behaviour of time-averaged characteristic function, which gives insight into rich memory structure of the studied processes. Moreover, we show applications of the ergodic criteria in Fourier space, determining the ergodicity of the generalised Langevin equation's solutions.

• 出版日期2017-8