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Questions tagged [mixing]

For questions about mixing in ergodic or probability theory.

In ergodic theory, there are two main notions of mixing: weak and strong mixing. They give how far is $\mu(A\cap T^{—n}B)$ from $\mu(A)\mu(B)$ if $(X,\mathcal,\mu,T)$ is a dynamical system.

In probability theory, mixing conditions are used to measure dependence between random variables.

149 questions
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mixing conditions for processes $(X_n, n\in \mathbb{N})$?

I hope this is not off topic, but I'm working with a process $(X_n, n\in \mathbb{N})$ and there's a theorem I want to use that is valid for certain strong mixing processes. The thing is, the usual definitions of mixing processes usually start off…
user127022
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Does asymptotic independence imply $\psi$-mixing?

Consider a stochastic process $(X_t:\, t\in\mathbb{Z})$ such that $X_t$ has marginal cdf $F$ for all $t$ and such that the following holds: for all $t$, $x$ and $y$ one has $$ P(X_{t+n}\leq x,\,X_t\leq y) = F(x)F(y) + C(x,y)\alpha^n$$ where $\alpha$…
user127022
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Mixing time with multiplicative rather than additive error?

First of all: I'm talking about Markov chains over finite spaces. Second: my grasp of formal notation is rather weak, and in general I'm pretty ignorant, so please bear with me. That said... All the (admittedly not too many) definitions of mixing…
Anonymous
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