Titlebook: Continuous-Time Markov Chains; An Applications-Orie William J. Anderson Book 1991 Springer-Verlag New York Inc. 1991 Branching process.Mark

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Continuous-Time Markov Chains978-1-4612-3038-0Series ISSN 0172-7397 Series E-ISSN 2197-568X

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https://doi.org/10.1007/978-3-322-94806-9called a continuous-time parameter Markov chain if for any finite set . of “times,” and corresponding set . of states in . such that ., we have . Equation (1.1) is called the Markov property. If for all ., . such that . and all .,. ε . the conditional probability . appearing on the right-hand side o

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Produktion und Unternehmungsformen such a stochastic process is uniquely determined by the one-step transition matrix . whose .,.th component is ., and an initial distribution vector ., whose .th component is .. Every probability involving the random variables of this chain can be determined from the finite-dimensional distributions

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Renate Neub?umer,Brigitte Hewelpect convergence of .(.) to the ergodic limits π.? We shall study two special types of ergodicity, the so-called strong ergodicity and exponential ergodicity. Of course, our main interest is always to characterize these properties in terms of the . matrix.

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,Konstruktive Ger?uschminderungsma?nahmen,ent the birth and death .-matrix of (3.2.1) given by.,where . is a set of birth-death parameters. Note again that . is conservative if and only if . = 0, and that if .. > 0, we are allowing the process to jump from state 0 directly to an absorbing state which, given the context here, is most conveni

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