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Markov Chains, Continuous Time
2020There 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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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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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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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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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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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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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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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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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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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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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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The assembly, regulation and function of the mitochondrial respiratory chain
Nature Reviews Molecular Cell Biology, 2021Irene Vercellino, Leonid A Sazanov
exaly