For questions about mixing in ergodic or probability theory.
-1
votes
1answer
36 views
Need help with the following:
Proof or counterexample:
a) if $T$ is ergodic, then $T^2$ is ergodic, b) if $T$ is strong mixing, then $T^2$ is strong mixing.
Thank you.
1
vote
1answer
59 views
Ergodic Theory (Weak Mixing)
If $T$ is weak mixing then we know that $T\times T \times \ldots \times T$ is also weak mixing.
Does anyone know if this is true for $T\times T \times \ldots$?
2
votes
1answer
46 views
Skewness of mixture density
I have the mixture density of two normal distributions:
\begin{align}
f(l)=\pi \phi(l;\mu_1,\sigma^2_1)+(1-\pi)\phi(l;\mu_2,\sigma^2_2)
\end{align}
The skewness is given by
\begin{align}
...
0
votes
1answer
33 views
difference between convolution of two densities and mixture density?
I am wondering about the difference of the convolution of two probability density functions and the mixture of those two. This is not the same right? But what is the difference and how can it be ...
3
votes
1answer
37 views
What is the relation between mixing (measure theory) and a map being topological mixing?
A map is said to be topogical mixing if given two sets $A$ and $B$ then there exists $N$ such that for all $n>N$
$f^n(A) \cap B$ is not empty
On the other hand, a measure \mu is said to be ...
1
vote
1answer
58 views
Is the product of two mixing random variables also mixing?
Question: Assume $X_t$ and $Y_t$ are random variables from the same probability space adapted to the filtration $\mathcal{F}_{-\infty}, ..., \mathcal{F}_t, ..., \mathcal{F}_{\infty}$. If $X_t$ and ...
10
votes
2answers
225 views
An equivalent condition for strong-mixing
For a measure-preserving (finite) system $(X,\mathcal{B},\mu,T)$, is it correct that the following are equivalent?
For every $A,B\in\mathcal{B}$ , $\displaystyle\lim_{n\rightarrow\infty}\mu(A\cap ...
0
votes
0answers
35 views
$\phi$ mixing for Gaussian process
I have a Gaussian random process(LTI filtered white noise) and I have to prove that it is $\phi$ mixing.
I tried to take the direct approach by taking the joint pdf of $x_s,x_{t+s}$ and find the ...
