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Construction of branching Markov processes with age and sign. (English) Zbl 0176.47902


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[1] ARIMA, R., AND Y. HASEGAWA, On global solutions for mixed problem of a semi-linear differential equation. Proc. Japan Acad. 39 (1963), 721-725. · Zbl 0173.11804 · doi:10.3792/pja/1195522891
[2] BARTLETT, M. S., An introduction to stochastic processes with special referenc to methods and application. Cambridge Univ. Press (1955). · Zbl 0068.11801
[3] DYNKIN, E. B., Markov processes. Springer (1965) · Zbl 0132.37901
[4] FUJITA, H., On the blowing up of solutions of the Cauchy problem for Ut=du+u1+a Journ. Fac. Sci. Univ. Tokyo, Sec. 1, 13 Part 2 (1966), 109-124. · Zbl 0163.34002
[5] HARRIS, T. E., The theory of branching processes. Springer (1963) · Zbl 0117.13002
[6] IKEDA, N., M. NAGASAWA, AND S. WATANABE, Branching Markov processes (t appear in J. Math. Kyoto Univ.). Abstracts: Proc. Japan Acad. 41 (1965), 816-821, 42 (1966), 252-257, 370-375, 380-384, 719-724, 1016-1021, 1022-1026. · Zbl 0224.60038 · doi:10.3792/pja/1195522254
[7] IKEDA, N., M. NAGASAWA, AND S. WATANABE, Foundation of Branching Marko processes. Seminar on Probability 23 (1966). (Japanese). · Zbl 0224.60038 · doi:10.3792/pja/1195522254
[8] Io, K., AND H. P. McKEAN. JR., Diffusion processes and their sample paths Springer (1965). · Zbl 0127.09503
[9] KATO, T., Nonlinear evolution equations in Banach spaces. Proc. Symp. in Appl Math. 17 (1965), 50-67. · Zbl 0173.17104
[10] KOLMOGOROV, A. N., I. PETROVSKY, AND N. PISCOUNOFF, Etude de equation d la diffusion avec croisance de la quantite de matiere et son application a un problem biologigue. Bull. State Univ. Moscow. Sect. A. Math. 1, Fasc. 6, (1937), 1-25. · Zbl 0018.32106
[11] LOEVE, M., Probability theory, third edition. D. van Nostrand (1963) · Zbl 0108.14202
[12] MEYER, P. A., Probability and Potentials. Blaisdell Pub. Co. (1966) · Zbl 0138.10401
[13] MOYAL, J. E., Discontinuous Markov processes. Acta Math. 98 (1957), 221-264 · Zbl 0078.32101 · doi:10.1007/BF02404475
[14] MOYAL, J. E., The general theory of stochastic population processes. Acta Math 108 (1962), 1-31. · Zbl 0128.40302 · doi:10.1007/BF02545761
[15] MOYAL, J. E., Multiplicative population processes. J. Appl. Prob. 1 (1964), 267-283 · Zbl 0203.17303 · doi:10.2307/3211859
[16] NAGASAWA, M., AND K. SATO, Some theorems on time change and killing o Markov processes. Kdai Math. Sem. Rep. 15 (1963), 195-219. · Zbl 0123.35202 · doi:10.2996/kmj/1138844812
[17] NAGASAWA, M., AND T. SIRAO, Probabilistic treatment of blowing up of solution for a non-linear integral equation. To appear in Trans. Amer. Math. Soc. · Zbl 0175.40702 · doi:10.2307/1995323
[18] NAGUMO, J., S. ARIMOTO, AND S. YOSIZAWA, An active pulse transmission line simulating nerve axon. Proceeding of the IRE 50 (1962), 2061-2070.
[19] SEGAL, L., Non-linear semi-groups. Ann. of Math. 78 (1963), 339-364 · Zbl 0204.16004 · doi:10.2307/1970347
[20] SIRAO, T., On signed Branching Markov Processes with age. (To appear in Nagoy Math. J. ). Abstract: Proc. Japan Acad. 42 (1966), 885-890. · Zbl 0174.49601
[21] SKOROHOD, A. V., Branching diffusion processes. Theory Prob. Appl. 9 (1964), 492-497 · Zbl 0264.60058 · doi:10.1137/1109059
[22] YAMAGUCHI, M., The asymptotic behaviour of the solution of a semi-linea partial differential equation related on an active pulse transmission line. Proc. Japan Acad. 39 (1963), 726-730. · Zbl 0173.11901 · doi:10.3792/pja/1195522892
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