0
votes
0answers
112 views

A doubt on Balaji Meyn's ergodic theorem paper

I have a question regarding the classic paper by Balaji and Meyn: "Multiplicative ergodicity and Large Deviations for an Irreducible Markov Chain". Consider a recurrent aperiodic irreducible Markov ...
4
votes
1answer
187 views

Birkhoff Ergodic Theorem and Ergodic Decomposition Theorem for Continuous-Time Markov Processes

I have a couple of questions regarding ergodicity for Markov processes in continuous time. (In particular, the first question seems like it should be particularly basic, and yet I haven't managed to ...
2
votes
0answers
77 views

Null sets visited infinitely often by trajectories of the shift dynamical system

Let $(G,\circ)$ be a Polish group, with identity $e$. Let $\Omega$ be the set of continuous functions $\omega:\mathbb{R} \to G$ such that $\omega(0)=e$. For each $t \in \mathbb{R}$, define the ...
2
votes
0answers
142 views

Markov operators and existence of ergodic measures

My question refers to the yesterday's question (see here) of John Learner and goes as follows: Can we deduce the existence of an ergodic measure if we know that an invariant measure exists, but the ...
5
votes
2answers
216 views

Liverani's CLT (a question)

Let $(\Omega,\mathcal{F},P)$ be a probability space where $\Omega$ is a complete separable metric space, let $T:\Omega\to \Omega$ ` be an ergodic transformation, let $\hat{T}:L^{2}_{_P}(\Omega)\to ...
2
votes
3answers
252 views

How long does it take a Brownian particle to achieve a uniform probability distribution across a space?

Imagine I have a point-like Brownian particle, with diffusion constant $D$, and I place it at some initial coordinate in a cage of known geometry. Assuming the volume $V$ of the cage is "everywhere" ...
3
votes
1answer
433 views

Ergodicity of Convoluted White Noise

I have a question regarding ergodicity in infinite dimensional spaces. Let $\mathcal{D}$ be the space of distributions on a Schwartz space, and let $\mu$ be the white noise process which exists by ...
12
votes
2answers
744 views

Non-integrable ergodic theory

Can anyone help me out with proofs/counterexamples? I'm working on an operator-valued multiplicative ergodic theorem and need what may(?) be a well-known fact. This fact (if true) would help me get ...
5
votes
0answers
374 views

Is there a continuous-time version of Kingman's subadditive decomposition theorem?

Kingman's subadditive ergodic theorem (see this article) states that if $x_{m,n}$ is a real valued process indexed on the set of pairs of non-negative integers $m < n$ satisfying: $x_{l,n} \le ...