A review of transient behavior in regular diffusion and birth-death processes
- 1 December 1964
- journal article
- review article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 1 (2), 247-266
- https://doi.org/10.2307/3211858
Abstract
Our concern is with passage times and rate of approach to ergodicity for two types of temporally homogeneous processes, doubly bounded diffusion processes in one dimension, and birth-death processes on the finite lattice. The passage time problems associated with these processes are of considerable practical interest, but for many important cases, e.g., the Uhlenbeck-Ornstein process, only formal solutions such as Laplace transforms (cf. Darling and Siegert, 1953) have been given, with limited numerical potential.Keywords
This publication has 10 references indexed in Scilit:
- The birth and death processes as diffusion processes;Published by Springer Nature ,2015
- An analytical approach to the differential equations of the birth-and-death process.The Michigan Mathematical Journal, 1962
- On Polynomial Expansions of Second-Order DistributionsJournal of the Society for Industrial and Applied Mathematics, 1962
- Eigenfunction Expansions Associated with Second-order Differential Equations, Part 1Physics Today, 1962
- Unitary Dilations of One-Parameter Semigroups of Markov Transition Operators, and the Corresponding Integral Representations for Markov Processes with a Countable Infinity of StatesProceedings of the London Mathematical Society, 1959
- The differential equations of birth-and-death processes, and the Stieltjes moment problemTransactions of the American Mathematical Society, 1957
- Spectral theory for the differential equations of simple birth and death processesPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1954
- The First Passage Problem for a Continuous Markov ProcessThe Annals of Mathematical Statistics, 1953
- The Parabolic Differential Equations and the Associated Semi-Groups of TransformationsAnnals of Mathematics, 1952
- On the First Passage Time Probability ProblemPhysical Review B, 1951