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Questions tagged [ergodic]

An ergodic dynamic system or stochastic process is one in which time averages agree with averages over the state space of the process.

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11
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1answer
745 views

How do you check ergodicity of a stochastic processes from its sample path(s)?

How do you check ergodicity of a wide-sense stationary stochastic processes from its sample path(s)? Can we check ergodicity from a single sample path? Or do we need multiple sample paths? One ...
4
votes
1answer
813 views

When is a ARMA(p,q) process ergodic?

We know that a ARMA(p,q) process is weakly stationary, iff there is no root of the characteristic polynomial of its AR part lying on the unit circle. But what is the necessary and sufficient ...
3
votes
1answer
869 views

Derivation of sample autocovariance

The autocovariance is defined as $$\gamma(t,s) = Cov(X_{t}, X_{s})=E[(X_{t}-\mu_{t})(X_{s}-\mu_{s})]$$ When we have a stationary process the only thing that matters is the lag between the variables: ...
3
votes
1answer
918 views

How to detect if Ergodicity, Stationarity and Martingale. dif. sequence?

I'm not sure, but I think I've read somewhere that because the Classical Linear Regression model assumes to have a random sample, when researchers they might not be in presence of a sample with that ...
2
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0answers
24 views

Is the Metropolis-Hastings kernel always aperiodic, irreducible and geometrically ergodic?

Let $(E,\mathcal E,\lambda)$ be a measure space, $Q$ be a Markov kernel on $(E,\mathcal E)$ with $$Q(x,B)=\int_B\lambda({\rm d}y)q(x,y)\;\;\;\text{for all }(x,B)\in E\times\mathcal E$$ for some ...
1
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1answer
44 views

Stationary Process Ergodicity

Can you give me an example of a stationary nonergodic stochastic process that is time continuous?
1
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2answers
114 views

Resource request : How to prove the output of a process is random variables?

I am reading through articles which present the spectral properties of chaotic systems such that they can be candidates for generating pseudo random binary sequences. One such article, is http://...