The decay function of nonhomogeneous birth-death processes, with application to mean-field models

The paper develops in different directions the method of the second author for estimation of the rate of exponential convergence of nonhomogeneous birth-death processes. Applying the method to mean-field models, we discover some phenomena related to their spectral gaps.

[1]  Alexander I. Zeifman.  Upper and lower bounds on the rate of convergence for nonhomogeneous birth and death processes , 1995 .

[2]  E. V. Doorn,et al.  Quasi-stationary distributions and convergence to quasi-stationarity of birth-death processes , 1991 .

[3]  Bernard Ycart.  The Philosophers' Process: An Ergodic Reversible Nearest Particle System , 1993 .

[4]  ON TRANSIENT BEHAVIOUR OF A NEAREST- NEIGHBOUR BIRTH-DEATH PROCESS ON A LATTICE , 1994 .

[5]  Florence Forbes,et al.  The philosophers' process on ladder graphs , 1996 .

[6]  W. J. Anderson.  Continuous-Time Markov Chains , 1991 .

[7]  Mu-Fa Chen,et al.  From Markov Chains to Non-Equilibrium Particle Systems , 1992 .

[8]  Harry Kesten,et al.  Random walks, Brownian motion and interacting particle systems : a festschrift in honor of Frank Spitzer , 1991 .

[9]  J. T. Cox,et al.  Nonlinear Voter Models , 1991 .

[10]  P. Diaconis,et al.  LOGARITHMIC SOBOLEV INEQUALITIES FOR FINITE MARKOV CHAINS , 1996 .

[11]  Neal Madras,et al.  The noisy voter model , 1995 .

[12]  van E.A. Doorn.  Conditions for exponential ergodicity and bounds for the Deacy parameters of a birth-death process , 1982 .

[13]  Alexander I. Zeifman.  Qualitative properties of inhomogeneous birth and death processes , 1991 .

[14]  P. Diaconis,et al.  Walks on generating sets of Abelian groups , 1996 .

[15]  T. Rolski,et al.  A general stochastic model of adsorption–desorption: Transient behavior , 1989 .

[16]  T. Liggett.  Interacting Particle Systems , 1985 .

[17]  Evaluation of the decay parameter for some specialized birth-death processes , 1992 .

[18]  C. Mufa,et al.  Estimation of spectral gap for Markov chains , 1996 .