Total variation approximation for quasi-equilibrium distributions, II

Ball, 2006, Asymptotic analysis of multiscale approximations to reaction networks, Ann. Appl. Probab., 16, 1925, 10.1214/105051606000000420 Barbour, 1976, Quasi-stationary distributions in Markov population processes, Adv. Appl. Probab., 8, 296, 10.2307/1425906 Barbour, 2010, Total variation approximation for quasi-stationary distributions, J. Appl. Probab., 47, 934, 10.1017/S0021900200007270 Beverton, 1957, vol. XIX Daley, 1999, vol. 15 Darling, 2008, Differential equation approximations for Markov chains, Probab. Surv., 5, 37, 10.1214/07-PS121 Darroch, 1965, On quasi-stationary distributions in absorbing discrete-time Markov chains, J. Appl. Probab., 2, 88, 10.1017/S0021900200031600 Hassell, 1975, Density-dependence in single-species populations, J. Anim. Ecol., 45, 283, 10.2307/3863 Kurtz, 1970, Solutions of ordinary differential equations as limits of pure jump Markov processes, J. Appl. Probab., 7, 49, 10.1017/S0021900200026929 Kurtz, 1971, Limit theorems for sequences of jump Markov processes approximating ordinary differential processes, J. Appl. Probab., 8, 344, 10.1017/S002190020003535X Kurtz, 1972, The relationship between stochastic and deterministic models in chemical reactions, J. Chem. Phys., 57, 2976, 10.1063/1.1678692 Maynard-Smith, 1973, The stability of predator–prey systems, Ecology, 54, 384, 10.2307/1934346 McNeil, 1973, Central limit analogues for Markov population processes, J. R. Stat. Soc. Ser. B, 35, 1 Meyn, 1993, Stability of Markovian processes III: Foster–Lyapunov criteria for continuous time processes, Adv. Appl. Probab., 25, 518, 10.1017/S0001867800025520 O’Hely, 2006, A diffusion approach to approximating preservation probabilities for gene duplicates, J. Math. Biol., 53, 215, 10.1007/s00285-006-0001-6 Ricker, 1954, Stock and recruitment, J. Fish. Res. Board Can., 11, 559, 10.1139/f54-039 Ridler-Rowe, 1978, On competition between two species, J. Appl. Probab., 15, 457, 10.1017/S0021900200045836 Roberts, 1996, Quantitative bounds for convergence rates of continuous time Markov processes, Electron. J. Probab., 1, 10.1214/EJP.v1-9 Ross, 2006, A stochastic metapopulation model accounting for habitat dynamics, J. Math. Biol., 52, 788, 10.1007/s00285-006-0372-8 Schach, 1971, Weak convergence results for a class of multivariate Markov processes, Ann. Math. Statist., 42, 451, 10.1214/aoms/1177693397 Seneta, 1966, On quasi-stationary distributions in discrete-time Markov chains with a denumerable infinity of states, J. Appl. Probab., 3, 403, 10.1017/S0021900200114226 van Doorn, 1991, Quasi-stationary distributions and convergence to quasi-stationarity of birth–death processes, Adv. Appl. Probab., 23, 683, 10.1017/S0001867800023880 Verhulst, 1838, Notice sur la loi que la population poursuit dans son accroissement, Corresp. Math. Phys., 10, 113 Yaglom, 1947, Certain limit theorems of the theory of branching processes, Dokl. Akad. Nauk SSSR (NS), 56, 795