http://www.bing.com:80/search?q=Markov+Chain+Transition+Matrix+PythonSearch resultshttp://www.bing.com:80/s/a/rsslogo.gifhttp://www.bing.com:80/search?q=Markov+Chain+Transition+Matrix+PythonCopyright © 2026 Microsoft. All rights reserved. These XML results may not be used, reproduced or transmitted in any manner or for any purpose other than rendering Bing results within an RSS aggregator for your personal, non-commercial use. Any other use of these results requires express written permission from Microsoft Corporation. By accessing this web page or using these results in any manner whatsoever, you agree to be bound by the foregoing restrictions.https://math.stackexchange.com/questions/5126032/probability-of-a-markov-chain-x-n-sim-u1-2-x-n-1-reaching-1024-within-50I am analyzing a discrete-time Markov chain that can grow exponentially but also suffers from frequent, severe drops. I want to find the exact probability that it reaches a certain threshold within aTue, 24 Mar 2026 20:44:00 GMThttps://math.stackexchange.com/questions/22982/what-is-the-difference-between-all-types-of-markov-chainsA 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 past and present that would be useful in saying something about the future is contained in the present state.Fri, 24 Apr 2026 01:02:00 GMThttps://math.stackexchange.com/questions/1185389/real-applications-of-markovs-inequalityMarkov's Inequality and its corollary Chebyshev's Inequality are extremely important in a wide variety of theoretical proofs, especially limit theorems. A previous answer provides an example.Thu, 23 Apr 2026 23:43:00 GMThttps://math.stackexchange.com/questions/1647761/what-are-some-modern-books-on-markov-chains-with-plenty-of-good-exercisesI 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 onTue, 21 Apr 2026 02:53:00 GMThttps://math.stackexchange.com/questions/3143502/intuition-behind-positive-recurrent-and-null-recurrent-markov-chainsFor irreducible Markov chains, if a state is recurrent, then every other state in the state space is automatically recurrent as well. This holds analogously for positive recurrence and null recurrence. In other words, communicating states share the same asymptotic returning behaviour.Wed, 22 Apr 2026 19:34:00 GMThttps://math.stackexchange.com/questions/544/what-is-a-markov-chain7 Markov chains, especially hidden Markov models are hugely important in computation linguistics. A hidden Markov model is one where we can't directly view the state, but we do have some information about what the state might be. For example, consider breaking down a sentence into what is called "parts of speech" such as verbs, adjectives, ect.Wed, 22 Apr 2026 17:11:00 GMThttps://math.stackexchange.com/questions/1270275/proofs-of-the-riesz-markov-kakutani-representation-theoremNote that this version of the Riesz-Markov-Kakutani theorem is much stronger than the usually stated one, which is concerned positive functionals on $\mathbb {R}$. The fact that the dual norm is the total variation one is equivalent to the fact that Baire measures are necessarily regular, a not so trivial fact proved in Halmos's Measure Theory.Tue, 21 Apr 2026 11:42:00 GMThttps://math.stackexchange.com/questions/4438235/periodic-and-aperiodic-states-in-a-markov-chain0 Imagine the following Markov chain: $$\begin {bmatrix} 0 & 0.5 & 0.5 \\ 1 & 0 & 0 \\ 1 & 0 & 0\end {bmatrix}$$ We always get back to state 1 in two time periods. So, state 1 is periodic and its period is 2. For states 2 and 3, the time it takes to get back to them can be 2, 4, 6, or any even number of periods.Wed, 22 Apr 2026 00:28:00 GMThttps://math.stackexchange.com/questions/1406918/markovian-property-vs-memoryless-propertyFinally, note that n-grams, for instance, illustrate a canonical example of the distinction above between Markov processes and the simplest possible memoryless processes.Sat, 25 Apr 2026 06:44:00 GMThttps://math.stackexchange.com/questions/266183/markov-process-vs-markov-chain-vs-random-process-vs-stochastic-process-vs-coMarkov processes and, consequently, Markov chains are both examples of stochastic processes. Random process and stochastic process are completely interchangeable (at least in many books on the subject).Thu, 23 Apr 2026 13:13:00 GMT