A review of transient behavior in regular diffusion and birth-death processes. Part II
- 1 December 1965
- journal article
- review article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 2 (2) , 405-428
- https://doi.org/10.1017/s0021900200108733
Abstract
(2) For chains with absorbing states, irreducibility on the set of non-absorbing states is required, i.e., we require that for any two states of this set n0, and nF there be a sequence of states n0, n1, …, nF for which θn0θn1 ‥ θnF ≠ 0. If for such non-absorbing states (5.5) is satisfied, the chain satisfies the Kolmogorov condition.Keywords
This publication has 11 references indexed in Scilit:
- A review of transient behavior in regular diffusion and birth-death processesJournal of Applied Probability, 1964
- Waiting Times When Queues are in TandemThe Annals of Mathematical Statistics, 1957
- The classification of birth and death processesTransactions of the American Mathematical Society, 1957
- The differential equations of birth-and-death processes, and the Stieltjes moment problemTransactions of the American Mathematical Society, 1957
- Diffusion processes in one dimensionTransactions of the American Mathematical Society, 1954
- The Parabolic Differential Equations and the Associated Semi-Groups of TransformationsAnnals of Mathematics, 1952
- On the First Passage Time Probability ProblemPhysical Review B, 1951
- On the Theory of the Brownian Motion IIReviews of Modern Physics, 1945
- Zur Theorie der stetigen zuf lligen ProzesseMathematische Annalen, 1933
- ber die analytischen Methoden in der WahrscheinlichkeitsrechnungMathematische Annalen, 1931