- Using a Continuous Time Markov Chain for Discrete Times
I am slightly confused In general, for a (discrete time) markov chain with transition matrix P P, this matrix can be time-dependent, although these markov chains are much less commonly studied Similarly, a (continuous time) markov process can have a time-dependent rate matrix Q Q, although this is much less commonly studied Do you assume you are not in this scenario?
- probability - How to prove that a Markov chain is transient . . .
Now, I am examining various scenarios pertaining to classifying the states of this Markov chain, for different possible values of p p I can see, by intuition, that for all values of p p where p ≠ 1 2 p ≠ 1 2, the Markov chain is transient
- Understanding the first step analysis of absorbing Markov chains
which is the key point of the so called "first step analysis" See for instance Chapter 3 in Karlin and Pinsky's Introduction to Stochastic Modeling But the book does not bother giving a proof of it Here is my question: How can one prove (*) using the definition of conditional probability and the Markov property?
- Expected time till absorption in specific state of a Markov chain
The modified Markov chain P~ P ~ exactly describes the transition probabilities for random walkers who will eventually end up state SG S G (unless they started in some other absorbing state) The expected time till absorption in this MC is exactly the quantity we set out to find, and we can compute it using another standard MC method
- Properties of Markov chains - Mathematics Stack Exchange
We covered Markov chains in class and after going through the details, I still have a few questions (I encourage you to give short answers to the question, as this may become very cumbersome other
- What is an example of a positive recurrent Continuous-time Markov Chain . . .
If by "embedded" you mean a Markov chain of the form Yn = X(n) Y n = X (n), n = 0, 1, 2, … n = 0, 1, 2,, where X X s a continuous-time Markov chain, then Y Y inherits the positive recurrence of X X This because the positive recurrence of X X implies the existence of a stationary (probability) distribution π π, and it is easy to check that π π is also a stationary distribution for Y Y
- stochastic processes - Does markovian property imply independence . . .
A stochastic process has the Markov property if the conditional probability distribution of future states of the process (conditional on both past and present states) depends only upon the present
- Expected number of flips vs probability in a Markov Chain
The probability you want is the probability, a8 = 3 5 a 8 = 3 5 , that Alice wins given that the Markov chain is in state 8 8, because that is the state it will be in when the game starts, which thus confirms the results of true blue anil's simulation
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