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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稱贊

978-1-4612-7772-9Springer-Verlag New York Inc. 1991

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https://doi.org/10.1007/978-3-322-94827-4In this chapter, we will be looking more closely at questions of nonuniqueness and uniqueness of .-functions. However, it will be more convenient to work with the Laplace transforms of the quantities involved, particularly the resolvent function in place of the transition function, rather than in the time domain as we did in Chapter 2.

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,übungsaufgaben und L?sungswege,A transition function . is said to be . if there exists a set . of strictly positive numbers such that. for all . and ..If, in addition, we have Σ.. = 1, then . is called symmetric. In either case, the set . is called the symmetrizing measure.

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Teubner Studienbücher MathematikIn this section, we investigate processes with state space . which are basically birth and death processes, but which also allow downward jumps called ., of arbitrary size.

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Classification of States and Invariant Measures,Let ., be a standard transition function, and let . denote a continuous-time Markov chain with state space ., and having . as its transition function.

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Reversibility, Monotonicity, and Other Properties,A transition function . is said to be . if there exists a set . of strictly positive numbers such that. for all . and ..If, in addition, we have Σ.. = 1, then . is called symmetric. In either case, the set . is called the symmetrizing measure.

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