All Questions

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 ...

Suppose, that we have sequence of i.i.d variables $X_1,\ldots,X_n$ taking values in $\mathbb{Z}_p$ such that $d_{TV}(X_1,U) < \delta$. How fast, in terms of $\delta$ and $n$ does the sum $X_1+\...

Let $\mathbb{F}_n$ be the free group (each elemen is in its reduced form) generated by the set $\Sigma_n = \{a_1, a_2, \cdots, a_n, a_1^{-1}, a_2^{-1}, \cdots, a_n^{-1}\}$ and let $e$ denote the ...

Consider a $p$ dimensional random variable with a discrete support. Consider a Markov transition kernel on the state space that is defined in terms of element-wise transition distributions. One can ...

For an ergodic Markov Chain $$ \frac{1}{N}\sum_{i=1}^n f(X_i) \rightarrow E_\pi[f] $$ where $\pi$ is the invariant distribution. I am also dealing with a Markovian process (a state space model to ...

Let $\tilde\kappa$ denote the transition kernel of the Markov chain generated by the Metropolis-Hastings algorithm with proposal kernel $\tilde Q$ and target distribution $\tilde\mu$. I want to ...