Convergence Property of Standard Transition Functions

Zhang, Hanjun; Mei, Qixiang; Lin, Xiang; Zhenting, Hou

doi:10.1007/978-1-4613-0265-0_4

Cited by 6 publications

(10 citation statements)

References 10 publications

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“…This means that the birth-death process is not strongly ergodic (see [10], [23], and [26]). Thus, by Theorem 3.1, the process is not strongly ergodic.…”

Section: Theorem 42 Assume That a = U∈s A(u) < ∞ Then The Q-procesmentioning

confidence: 99%

A Class of Multidimensional Q-Processes

Zhang

2007

J. Appl. Probab.

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“…This means that the birth-death process is not strongly ergodic (see [10], [23], and [26]). Thus, by Theorem 3.1, the process is not strongly ergodic.…”

Section: Theorem 42 Assume That a = U∈s A(u) < ∞ Then The Q-procesmentioning

confidence: 99%

A Class of Multidimensional Q-Processes

Zhang

2007

J. Appl. Probab.

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“…It is known that statements (i) and (ii) of Theorem 1.4 are equivalent (see [15], [16]) and so too are (iii) and (iv), by Theorems 1.1 and 1.2. To prove the equivalence of (ii) and (iii), we will compute T .…”

Section: Proof Of Theorem 14 and An Application To Orthogonal Polynomentioning

confidence: 95%

The eigentime identity for continuous-time ergodic Markov chains

Mao¹

2004

Journal of Applied Probability

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The eigentime identity is proved for continuous-time reversible Markov chains with Markov generator L. When the essential spectrum is empty, let {0 = λ0 < λ1 ≤ λ2 ≤ ···} be the whole spectrum of L in L2. Then ∑n≥1 λn-1 < ∞ implies the existence of the spectral gap α of L in L∞. Explicit formulae are presented in the case of birth–death processes and from these formulae it is proved that ∑n≥1 λn-1 < ∞ if and only if α > 0.

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“…Remarks 2.5. (i) Under the restriction of stochastic monotonicity, [8] discusses the uniformly polynomial convergence for time-continuous Markov chains in terms of Feller transition functions. The convergence means that there exist two constants v > 0 and C > 0 so that sup i,j ∈E t v |p ij (t) − π j | ≤ C for all t ≥ 0.…”

Section: Corollary 24 a Regular Birth-death Process Is Strongly Ergmentioning

confidence: 99%

“…It should be pointed out that for birth-death processes, which are special cases of singlebirth processes, Theorem 1.1 and the second part of Theorem 1.2 have been obtained in [8] and [6] respectively, using a different approach. See Remark 2.5(i) and Remark 3.1(i) for further comments.…”

Section: Introductionmentioning

confidence: 99%

Strong ergodicity for single-birth processes

Zhang¹

2001

Journal of Applied Probability

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An explicit and computable criterion for strong ergodicity of single-birth processes is presented. As an application, some sufficient conditions are obtained for strong ergodicity of an extended class of continuous-time branching processes and multi-dimensional Q-processes by comparison methods respectively. Consequently strong ergodicity of the Q-process corresponding to the finite-dimensional Schlögl model is proven.

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Convergence Property of Standard Transition Functions

Cited by 6 publications

References 10 publications

A Class of Multidimensional Q-Processes

A Class of Multidimensional Q-Processes

The eigentime identity for continuous-time ergodic Markov chains

Strong ergodicity for single-birth processes

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