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Continuous Time Markov Chains

2016
A queueing system can be described in terms of servers and a flow of clients who access servers and are served according to some pre-established rules. The clients after service can either stay in the system or leave it, also according to some established rules.
Francesca Biagini, Massimo Campanino
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Continuous-Time Markov Chains

1992
In this chapter we again develop continuous-time stochastic processes having Markov properties.
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Markov Chains, Continuous Time

2020
There are two complementary points of view in the study of continuous-time hmcs. The traditional approach attempts to mimic the discrete-time theory. It is based on the transition semigroup, the continuous-time analogue of the iterates of the transition matrix in discrete time, and the principal mathematical object is then the infinitesimal generator.
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Continuous-Time Markov Chains

2013
In this chapter we start the study of continuous-time stochastic processes, which are families \((X_{t})_{t\in\mathbb{R}_{+}}\) of random variables indexed by \(\mathbb{R}_{+}\). Our aim is to make the transition from discrete to continuous-time Markov chains, the main difference between the two settings being the replacement of the transition matrix ...
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Continuous time Markov chains

2010
This chapter introduces the subject of continuous-time Markov chains [23, 52, 59, 80, 106, 107, 118, 152]. In practice, continuous-time chains are more useful than discrete-time chains. For one thing, continuous-time chains permit variation in the waiting times for transitions between neighboring states.
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Continuous-Time Markov Chains

2023
Julio B. Clempner, Alexander Poznyak
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Continuous-Time Markov Chains

2009
A continuous-time Markov chain (CTMC) is a discrete-time Markov chain with the modification that, instead of spending one time unit in a state, it remains in a state for an exponentially distributed time whose rate depends on the state. The methodology of CTMCs is based on properties of renewal and Poisson processes as well as discrete-time chains ...
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Continuous-time Markov chains

2017
As in discrete time, continuous-time Markov chains are stochastic processes in which the future depends on the past only through the present, or equivalently, given the present, past, and future are independent. Since there is no next time when time is continuous, the process is now characterized by transition rates instead of transition probabilities.
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Continuous-time Markov chains

1997
In this chapter, we consider the continuous-time analogs of discrete-time Markov chains. As in the discrete-time case, they are characterized by the Markov property that, given the present state, the future of the process is stochastically independent of the past.
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