Mode, C.J. (1971) Multitype branching processes: theory and applications (American Elsevier Publishing Company, New York). Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Backbends in Directed Percolation - Rahul Roy Anish (Correct)
....j n j = 1 now corresponds to the survival of the multi type branching process. But by the Perron Frobenius Theorem, the offspring matrix M n;p has a positive real eigenvalue n;p such that n;p = maxfj j : is an eigenvalue of M n;p g; and it is well known (see for example [9]) that the process will survive with 5 positive probability if and only if n;p 1. Thus, n = n;1 ) Gamma1 Using MATLAB we obtain the following values (to 4 decimal places from n = 1 onwards) 4 = 0:3478: We can follow a similar approach for n paths, this time saying ....
Mode, C.J. (1971) Multitype branching processes: theory and applications (American Elsevier Publishing Company, New York).
Branching Processes - Athreya, Vidyashankar (1999) (113 citations) (Correct)
....e subject started to take off in the late 1940 s and 50 s with the work of Kolmogorov, Yaglom, and Sevastyanov and their students in Russia and Harris and Bellman in the United States. Harris authoritative book [38] appeared in 1960 and stimulated much re search on the subject. The book by Mode [51] on multitype branching processes came out in 1969. Then in 1972 the book by Athreya and Ney [23] was published. Jagers [43] wrote a book on branching processes with biological applications in mind. On a more ab stract level, the book by Asmussen and Herring [4] came out in 1982. Senata and Heyde ....
....the work of Swedish school led by Jagers on general branchging processes with greater level of dependencies. For an account of this see Jagers [44] and the references therein. We also have not dea lt with the problems of statistical inference in branching processes. Apart from the book of Guttorp [51], the work of Dion [34] with its extensive bibiliography is very helpful. We end this with an outline of the rest of the paper. The next section deals with the socalled simple branching process of single type. This is followed by the multitype case. Continuous time branching process of single type ....
Mode,C.J.(1971): Multitype branching processes: Theory and applications, American Elsevier Publishing Co. Inc, New York.
Backbends in Directed Percolation - Roy, Sarkar, White (1997) (Correct)
....j C 0 n j = 1 now corresponds to the survival of the multi type branching process. But by the Perron Frobenius Theorem, the offspring matrix M n;p has a positive real eigenvalue n;p such that n;p = maxfj j : is an eigenvalue of M n;p g; and it is well known (see for example [9]) that the process will survive with positive probability if and only if n;p 1. Thus, p 0 n = n;1 ) Gamma1 : Using MATLAB we obtain the following values (to 4 decimal places from n = 1 onwards) p 0 0 = 0:5; p 0 1 = 0:4142; p 0 2 = 0:3761; p 0 3 = 0:3576; ....
Mode, C.J. (1971) Multitype branching processes: theory and applications (American Elsevier Publishing Company, New York).
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