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・ Markov chain mixing time
・ Markov chain Monte Carlo
・ Markov chains on a measurable state space
・ Markov decision process
・ Markov information source
・ Markov kernel
・ Markov logic network
・ Markov model
・ Markov number
・ Markov partition
・ Markov perfect equilibrium
・ Markov process
・ Markov Processes International
・ Markov property
・ Markov random field
Markov renewal process
・ Markov reward model
・ Markov Reward Model Checker
・ Markov spectrum
・ Markov strategy
・ Markov switching multifractal
・ Markov tree
・ Markov's inequality
・ Markov's principle
・ Markova Crkva
・ Markova Sušica
・ Markovac
・ Markovac (Mladenovac)
・ Markovac (Velika Plana)
・ Markovac (Vršac)


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Markov renewal process : ウィキペディア英語版
Markov renewal process
In probability and statistics a Markov renewal process is a random process that generalizes the notion of Markov jump processes. Other random processes like Markov chain, Poisson process, and renewal process can be derived as a special case of an MRP (Markov renewal process).
==Definition==
Consider a state space \mathrm. Consider a set of random variables (X_n,T_n), where T_n are the jump times and X_n are the associated states in the Markov chain (see Figure). Let the inter-arrival time, \tau_n=T_n-T_. Then the sequence (X''n'', T''n'') is called a Markov renewal process if
:\Pr(\tau_\le t, X_=j|(X_0, T_0), (X_1, T_1),\ldots, (X_n=i, T_n))
: =\Pr(\tau_\le t, X_=j|X_n=i)\, \forall n \ge1,t\ge0, i,j \in \mathrm

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