Hostname: page-component-848d4c4894-pftt2 Total loading time: 0 Render date: 2024-05-19T02:18:40.625Z Has data issue: false hasContentIssue false
  • English
  • Français

On Signed Branching Markov Processes with Age

Published online by Cambridge University Press:  22 January 2016

Tunekiti Sirao
Tunekiti Sirao*
Affiliation:
Nagoya University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Many authors have considered branching Markov processes for the probabilistic treatment of semi-linear equations. Recently J.E. Moyal [11], [12] gave a formulation for a wide class of branching processes. A similar idea was used in A.V. Skorohod [18] and N. Ikeda-M. Nagasawa-S. Watanabe [4]-[7]. Applying their method, we shall consider in this paper the following problems (A) and (B).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 32 , June 1968 , pp. 155 - 225
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1968

References

[1] Dynkin, E.B.: Markov processes. Springer 1965.Google Scholar
[2] Dynkin, E.B.: Markov processes and semi-group of operators. Th. of Prob. & its appl. Vol. 1 (1956), pp. 22–33.Google Scholar
[3] Hunt, G.A.: Markov processes and potentials II. III. Jour. Math., Vol. 2 (1958), pp. 151–213.Google Scholar
[4] Ikeda, N., Nagasawa, M. and Watanabe, S.: Foundation of branching Markov processes. Seminar on Probability, Vol. 23 (1966), (in Japanese).Google Scholar
[5] Ikeda, N., Nagasawa, M. and Watanabe, S.: On branching Markov processes. Proc. Japan Acad. Vol. 41 (1965), pp. 816–821.Google Scholar
[6] Ikeda, N., Nagasawa, M. and Watanabe, S.: Fundamental equations of branching Markov processes. Proc. Japan Acad. Vol. 42 (1966), pp. 252–257.Google Scholar
[7] Ikeda, N., Nagasawa, M. and Watanabe, S.: Branching Markov Processes, (to appear).Google Scholar
[8] Ito, K. and McKean, H.P. Jr.: Diffusion processes and their sample paths. Springer, 1965.Google Scholar
[9] Kolmogoroff, A., Petrovsky, I. and Piscounoff, N.: Etude de l’équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique. Bull. l’Univ. Moscou, Vol. 1, Fase. 6, pp. 1–25.Google Scholar
[10] Moyal, J.E.: Discontinuous Markov processes. Acta. Math., Vol. 98 (1957), pp. 221–264.Google Scholar
[11] Moyal, J.E.: The general theory of stochastic population processes. Acta. Math., Vol. 108 (1962), pp. 1–32.Google Scholar
[12] Moyal, J.E.: Multiplicative population processes. Jour. Appl. Prob. Vol. 1 (1964), pp. 267–283.Google Scholar
[13] Nagasawa, M.: Construction of branching Markov processes with age and sign (to appear).Google Scholar
[14] Nagasawa, M. and Sirao, T.: Probabilistic treatment of blowing up of solutions for a non-linear integral equation (to appear).Google Scholar
[15] Ryser, H.J.: Combinatorial Mathematics. John Wiely Sons, 1963.Google Scholar
[16] Sirao, T.: A probabilistic treatment of semi-linear parabolic equations. Proc. Japan Acad. Vol. 42 (1966), pp. 885–890.Google Scholar
[17] Sirao, T.: Remarks on the Moyal’s construction of Markov processes, (to appear).Google Scholar
[18] Skorohod, A.V.: Branching diffusion processes. Th. of Prob. & its Appl. Vol. 9 (1964), pp. 492–497.Google Scholar