1
vote
0answers
50 views

iterates of generalized matrix system

This may be somewhat of an underspecified question but I'll nonetheless give it a try. In the context of applied work, I've recently come across systems of the form $$ ...
2
votes
1answer
124 views

If $P$ is an invertible transition probability matrix, does $P^{-1}[i,j]$ have any interesting meaning?

Suppose we have a Markov chain transition probability matrix $P$ that is invertible, i.e., $P^{-1}$ exists. Question: Does there exist a meaningful interpretation of the $(i,j)$ entry in $P^{-1}$? ...
0
votes
1answer
179 views

Continuous Markov chain, finding the stationary distribution

I am given a system of the form $x'(t)=Ax(t)$ where $A\in M_{3}(\mathbb{R})$ is a diagonalizable matrix and an initial condition $x(0)=\begin{pmatrix}1/3\\ 2/3\\ 0 \end{pmatrix}$ and I am being asked ...
3
votes
2answers
305 views

How can a Markov chain be written as a measure-preserving dynamic system

From http://masi.cscs.lsa.umich.edu/~crshalizi/notabene/ergodic-theory.html irreducible Markov chains with finite state spaces are ergodic processes, since they have a unique invariant ...
2
votes
0answers
172 views

Ergodicity and mixing

From MathOverflow, R W said: Unfortunately, the way the term "ergodic" is used in the theory of (finite) Markov chains is completely misleading from the point of view of general ergodic ...
1
vote
1answer
88 views

Shuffling cards and the horseshoe map

I wonder if there is a connection between the dynamics of repeated cut & shuffle operations on a deck of cards, and topological chaotic maps such as the horseshoe map? I ask this entirely naively. ...