منابع مشابه
Ergodic properties of Markov processes
In these notes we discuss Markov processes, in particular stochastic differential equations (SDE) and develop some tools to analyze their long-time behavior. There are several ways to analyze such properties, and our point of view will be to use systematically Liapunov functions which allow a nice characterization of the ergodic properties. In this we follow, at least in spirit, the excellent b...
متن کاملErgodic Properties of Markov Processes
Markov processes describe the time-evolution of random systems that do not have any memory. Let us demonstrate what we mean by this with the following example. Consider a switch that has two states: on and off. At the beginning of the experiment, the switch is on. Every minute after that, we throw a dice. If the dice shows 6, we flip the switch, otherwise we leave it as it is. The state of the ...
متن کاملErgodic properties of countable extensions
Roth, Samuel Joshua PhD, Purdue University, May 2015. Ergodic Properties of Countable Extensions. Major Professor: Micha l Misiurewicz. First, we study countably piecewise continuous, piecewise monotone interval maps. We establish a necessary and sufficient criterion for the existence of a non-decreasing semiconjugacy to an interval map of constant slope in terms of the existence of an eigenvec...
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If the rotation angle α is irrational, then ζ is generating for T (see [4]) and the partition ζn = ζ ∨Tζ ∨···∨Tn−1ζ is made out of 2n arcs. This can be easily realized by induction: when passing from ζn−1 to ζn one has to add to the endpoints of the arcs belonging to ζn−1 the two new points Tn(0) and Tn(1/2) (for rational α, say α = p/q, the partition ζn has precisely 2q arcs for all n≥ q). Thu...
متن کاملErgodic Properties of Microcanonical Observables
The problem of the existence of a Strong Stochasticity Threshold in the FPU-β model is reconsidered, using suitable microcanonical observables of thermodynamic nature, like the temperature and the specific heat. Explicit expressions for these observables are obtained by exploiting rigorous methods of differential geometry. Measurements of the corresponding temporal autocorrelation functions loc...
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ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 2014
ISSN: 0143-3857,1469-4417
DOI: 10.1017/etds.2014.79