From 281cc66ff2c41db75a25d981446bf26dcf58e494 Mon Sep 17 00:00:00 2001 From: lrjconan Date: Sat, 6 Jul 2024 10:53:35 -0700 Subject: [PATCH] Update 2023-07-12-markov-chains.md Change image path and header. --- _posts/2023-07-12-markov-chains.md | 21 ++++++++++++++------- 1 file changed, 14 insertions(+), 7 deletions(-) diff --git a/_posts/2023-07-12-markov-chains.md b/_posts/2023-07-12-markov-chains.md index 31f85b7..2104d8d 100644 --- a/_posts/2023-07-12-markov-chains.md +++ b/_posts/2023-07-12-markov-chains.md @@ -1,9 +1,16 @@ --- -title: Discrete Markov Chains -date: 2023-07-12 18:00:00 -tags: Markov Chains -categories: Reading Group -mathjax: true +layout: distill +title: Markov Chains +description: An introduction to Markov Chains. +tags: probability, random process, Markov Chains +giscus_comments: true +date: 2023-07-12 +featured: true + +authors: + - name: Xue Yu + affiliations: + name: Renmin University of China/UBC --- @@ -89,7 +96,7 @@ Let $\mu_{i} = \sum_{t \geq 1} t \cdot r_{i,i}^{t}$ denote the expected time to Here we give an example of a Markov chain that has null recurrent states. Consider the following markov chain whose states are the positive integers. -![Fig. 1. An example of a Markov chain that has null recurrent states ](./Markov-Chains/image.png) +![Fig. 1. An example of a Markov chain that has null recurrent states ](assets/img/markov_chains/image.png) Starting at state 1, the probability of not having returned to state 1 within the first $t$ steps is $$ @@ -128,7 +135,7 @@ A state $i$ is periodic means that for $s = k, 2k, 3k,...$, $P(X_{t+s}= j | X_t Consider the two-state “broken printer” Markov chain: -![Transition diagram for the two-state broken printer chain](./Markov-Chains/2023-07-22-11-00-52.png) +![Transition diagram for the two-state broken printer chain](assets/img/markov_chains/2023-07-22-11-00-52.png) There are two state (0 and 1) in this Markov chain, and assume that the initial distribution is $$