Critical branching diffusions : proper normalization and conditioned limit

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1. [1] M.I. Goldstein and F.M. Hoppe, Critical multitype branching processes with infinite variance. J. Math. Anal. Appl., t. 65, p. 676-686. Zbl0408.60082MR510478
2. [2] M.I. Goldstein and F.M. Hoppe, Necessary conditions for normed convergence of critical multitype Bienaymé-Galton-Watson processes without variance. J. Multivar. Anal., t. 8, 1978, p. 55-62. Zbl0382.60092MR483051
3. [3] H. Hering, Uniform primitivity of semigroups generated by perturbed elliptic differential operators. Math. Proc. Camb. Phil. Soc., t. 83, 1978, p. 261-268. Zbl0374.47021MR467044
4. [4] H. Hering, Minimal moment conditions in the limit theory for general Markov branching processes. Ann. Inst. Henri Poincaré, Sér. B, t. 13, 1978, p. 299-319. Zbl0391.60077MR488340
5. [5] H. Hering, Multigroup branching diffusions. Advances in Probability, t. 5, 1978, p. 177-217. Zbl0408.60084MR517535
6. [6] N. Ikeda, M. Nagasawa and S. Watanabe, Branching Markov processes I, II, III, J. Math. Kyoto Univ., t. 8, 1968, p. 233-278, p. 365-410; t. 9, 1969, p. 95-160. Zbl0233.60068MR232439
7. [7] E.E. Kohlbecker, Weak asymptotic properties of partitions. Trans. Amer. Math. Soc., t. 88, 1958, p. 346-365. Zbl0173.04203MR95808
8. [8] J. Lamperti, An occupation time theorem for a class of stochastic processes, Trans. Amer. Math. Soc., t. 88, 1958, p. 380-387. Zbl0228.60046MR94863
9. [9] H. Rubin and D. Vere-Jones, Domain of attraction for the subcritical Galton-Watson branching process. J. Appl. Prob., t. 5, 1968, p. 216-219. Zbl0181.20601MR228074
10. [10] T. Savits, The explosion problem for branching Markov process. Osaka J. Math., t. 6, 1969, p. 375-395. Zbl0216.47104MR282426
11. [11] E. Seneta, Regularly Varying Functions. SpringerLecture Notes in Mathematics, New York, 1976, p. 508. Zbl0324.26002MR453936
12. [12] R.S. Slack, A branching process with mean one and possibly infinite variance. Z. Wahrsch., t. 9, 1968, p. 139-145. Zbl0164.47002MR228077
13. [13] R.S. Slack, Further notes on branching processes with mean one. Z. Wahrsch., t. 25, 1972, p. 31-38. Zbl0236.60056MR331539
14. [14] V.A. Vatutin, A limit theorem for a critical Bellman-Harris branching process with several types of particles and infinite second moments. Theor. Probability Appl., t. 23, 1978, p. 776-778. Zbl0422.60062MR516277
15. [15] V.M. Zolotarev, More exact statements of several theorems in the theory of branching processes. Theor. Probability Appl., t. 2, 1957, p. 245-253. Zbl0089.34202MR96321