On exponential ergodicity and spectral structure for birth-death processes, II

AbstractIn Part I, Feller's boundary theory was described with simple conditions for process classification. The implications of this boundary classification scheme for spectral structure and exponential ergodicity are examined in Part II. Conditions under which the spectral span is finite or infinite are established. A time-dependent norm is exhibited describing the exponentiality of the convergence and its uniformity. Specific systems are discussed in detail: Contents:1.7. Spectral structure for the M/M/I process2.8. Exponential ergodicity for processes with entrance, exit, and regular boundaries3.9. Exponential ergodicity for processes with natural boundaries4.10. Uniformity of exponential convergence5.11. Finite and Infinite spectral span6.12. Skip-free processes on the full lattic