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Some modified branching diffusion models. (English) Zbl 0369.60103

MSC:
60J85 Applications of branching processes
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
92D25 Population dynamics (general)
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[1] Athreya, K.B.; Ney, P., Branching processes, (1972), Springer Berlin · Zbl 0259.60002
[2] Mode, C.J., Multitype branching processes, (1971), American Elsevier New York · Zbl 0219.60061
[3] Hering, H., Limit theorem for critical branching diffusion processes with absorbing barriers, Math. biosci., 19, 355-370, (1974) · Zbl 0282.60053
[4] Asmussen, S.; Hering, H., Strong limit theorems for general supercritical branching processes with applications to branching diffusions, Z. wahrscheinlichkeitstheorie verw. geb., 36, 195-212, (1976) · Zbl 0325.60081
[5] Hering, H., Subcritical branching diffusions, Compos. math., 34, (1977) · Zbl 0368.60093
[6] Hering, H., Minimal moment conditions in the limit theory for Markov branching processes, Ann. inst. H. PoincarĂ©, sec. B, 13, (1977) · Zbl 0391.60077
[7] Ikeda, N.; Nagasawa, M.; Watanabe, S.; Ikeda, N.; Nagasawa, M.; Watanabe, S.; Ikeda, N.; Nagasawa, M.; Watanabe, S., Branching Markov processes I-III, J. math. Kyoto univ., Math. Kyoto univ., J. math. Kyoto univ., 9, 95-160, (1969) · Zbl 0233.60070
[8] Breiman, L., Probability, (1968), Addison-Wesley Reading, Mass · Zbl 0174.48801
[9] Hering, H., Refined positivity theorem for semigroups generated by perturbed elliptic differential operators, Math. proc. cambr. phil. soc., (1976), subm. to
[10] Dynkin, E.B., Markov processes I-II, (1965), Springer Berlin · Zbl 0132.37901
[11] Harris, T.E., The theory of branching processes, (1963), Springer Berlin · Zbl 0117.13002
[12] Asmussen, S., Almost sure behavior of linear functionals of supercritical branching processes, Trans. am. math. soc., (1977) · Zbl 0376.60083
[13] Asmussen, S.; Hering, H., Strong limit theorems for supercritical immigration-branching processes, Math. scand., 39, 327-342, (1976) · Zbl 0348.60117
[14] Hering, H., Asymptotic behaviour of immigration-branching processes with general set of types. I: critical branching part, Adv. appl. probab., 5, 391-416, (1973) · Zbl 0283.60085
[15] Bartlett, M.S., Deterministic and stochastic models for recurrent epidemics, Proc. 3rd Berkeley symp. math. stat. probab., 4, 81-109, (1956) · Zbl 0070.15004
[16] Neyman, J.; Scott, E.L., A stochastic model of epidemics, (), 45-85 · Zbl 0161.39801
[17] Bartoszynski, R., Branching processes and the theory of epidemics, Proc. 5th Berkeley symp. math. stat. probab., 4, 259-269, (1967)
[18] Griffiths, D.A., A bivariate birth-death process which approximates to the spread of a disease involving a vector, J. appl. probab., 10, 15-26, (1972) · Zbl 0246.92004
[19] Radcliffe, J., The initial geographical spread of host-vector and carrierborne epidemics, J. appl. probab., 10, 703-717, (1973) · Zbl 0281.60101
[20] Radcliffe, J., The effect of the length of incubation period on the velocity of propagation of an epidemic wave, Math. biosci., 19, 257-262, (1974) · Zbl 0311.92017
[21] Radcliffe, J., The convergence of a position-dependent branching process used as an approximation to a model describing the spread of an epidemic, J. appl. probab., 13, 338-344, (1976) · Zbl 0349.92032
[22] Weinberg, A.M.; Wigner, E.P., The physical theory of neutron chain reactors, (1958), Univ. of Chic. Press
[23] Bailey, N.T.J., The mathematical theory of infectious diseases and its applications, (1975), Griffin London · Zbl 0115.37202
[24] Davis, A.W.; Davis, A.W., Branching diffusion processes with no absorbing boundary I-II, J. math. anal. appl., J. math. anal. appl., 19, 1-25, (1967) · Zbl 0189.51203
[25] Kaplan, N.; Asmussen, S., Branching random walks II, Stochastic proc. appl., 4, 15-31, (1976) · Zbl 0322.60065
[26] Gantmacher, F.R., Matrizenrechnung II, (1959), VEB Dtsch. Verlag der Wiss Berlin · Zbl 0085.00904
[27] Cinlar, E., Markov renewal theory, Adv. appl. probab., 1, 123-187, (1969) · Zbl 0212.49601
[28] Crump, K.S., On systems of renewal equations, J. math. anal. appl, 30, 425-434, (1970) · Zbl 0198.22502
[29] Cinlar, E., Introduction to stochastic processes, (1975), Prentice-Hall Englewood Cliffs · Zbl 0341.60019
[30] Shurenkov, V.M., A note on a multidimensional renewal equation, Theory probab. appl, 20, 833-836, (1975) · Zbl 0363.60077
[31] Ryan, T.A., A multidimensional renewal theorem, Ann. probab., 4, 656-661, (1976) · Zbl 0379.60090
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