I would like to know what books people currently like in Markov Chains (with syllabus comprising discrete MC, stationary distributions, etc.), that contain many good exercises. Some such book on

Jan 1, 2023 · For two states $x,y$ in $E$, let $p^n (x,y)$ denote the $n$ -step Markov chain transition probability from $x$ to $y$. Then the period of a point $x$ is the greatest common divisor of all …

Apr 25, 2017 · A Markov process is basically a stochastic process in which the past history of the process is irrelevant if you know the current system state. In other words, all information about the …

Stochastic processes (with either discrete or continuous time dependence) on a discrete (finite or countably infinite) state space in which the distribution of the next state depends only on the current …

Jun 17, 2022 · Then it's a Markov Chain it's a Markov Chain . If you use another definition : From the first line of each random walk and Markov Chain , I think a Markov chain models a type of random walk , …

Apr 14, 2024 · Theorem 1 (The Fundamental Theorem of Markov Chains): Let X0,X1, … X 0, X 1, be a Markov chain over a finite state space, with transition matrix P P. Suppose that the chain is …

Mar 26, 2021 · Is this a type of Markov operator? (The infinitesimal generator is also an operator on measurable functions). What's the equivalence between these two definitions and what's the intuition …

Almost, but you need "greater than or equal to." We have: $$ H (X|Y) = H (X|Y,Z) \leq H (X|Z) $$ where the first equality is from the Markov structure and the final inequality is because conditioning reduces …

Even stochastic processes arising from Newtonian physics don't have the Markov property, because parts of the state (say, microscopic degrees of freedom) tend not to be observed or included in the …

Sep 30, 2023 · A Gauss-Markov process is a random process that is both a Gaussian process and a Markov process. What is the difference between them? Are there Gauss-Markov processes that are …