D. P. Kennedy, The Galton-Watson process conditioned on the total progeny, J. Appl. Prob. 12 (1975), 800-806. Home/Search Document Not in Database Summary Related Articles Check |
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Ideals In A Forest, One-Way Infinite Binary Trees And The.. - Janson (Correct)
....(for critical and subcritical processes) it is the process conditioned on living forever. Similarly, it is easily shown that for a critical Galton Watson process with finite o#spring variance, the size biased process is the limit as of the process conditioned on the total progeny being n [7, 1]. In the case of random binary trees, this conditioning yields B n , and we recover Lemma 5.2. Having proved that both the trees B n and the functional Q(B n ) defined on them converge in distribution, it is natural to try to interpret the limit in Theorem 3.1 as Q(B# ) for an extension of Q to ....
D.P. Kennedy, The Galton--Watson process conditioned on the total progeny. J. Appl. Probab. 12 (1975), no. 4, 800--806.
A Random Walk Approach to Galton-Watson Trees - Bennies, Kersting (1999) (1 citation) (Correct)
....= j p j = P k k p k is a distribution, which fulfils all the assumptions of the corollary. Also CGW (n) trees from (p j ) and 14 (q j ) coincide in distribution. Therefore TM converges in distribution to a GW tree with offspring distribution (q j ) This device goes back to Kennedy [18]) 5 Lines of ancestors and the contour of a CGW (n) tree Let m be an individual in the k th generation. Then we denote by m 1 m 2 : m k 1 its ancestral line, i.e. m 1 = m, m 2 is the father of m, m 3 its grandfather, and so on. It is convenient to set m k 1 = 1. In this section ....
Kennedy, D.P. (1975), The Galton-Watson process conditioned on the total progeny. J. Appl. Prob. 12, 800-806
On The Profile Of Random Trees - Drmota, Gittenberger (1996) (2 citations) (Correct)
....we have l n (t) w Gamma 0 ( oe 2 l i oe 2 t j in C[0; 1) as n 1. The density of local time. The one dimensional density of (l(t) t 0) at t = ae is well studied. There are several representations available in the literature: Using the theory of branching processes Kennedy [15] and Kolchin [18, Theorem 2.5.6] obtained f ae (x) x 4 1 Z 0 (1 Gamma s) Gamma 3 2 e Gamma x 2 ae 2 8(1 Gammas) g 2ae i x 2 ; s j ds; 1.5) where g r (z; s) is the density of a distribution given by its characteristic function: r ( 1 ; 2 ) 2 4 sinh(r p Gamma2i 2 ....
D. P. Kennedy, The Galton-Watson process conditioned on the total progeny, J. Appl. Prob. 12 (1975), 800--806.
On Nodes Of Given Degree In Random Trees - Drmota (1996) (2 citations) (Correct)
....conditioned on the total progeny jX j is determined by P fX = T jjX j = ng and it is easily seen that this distribution coincides with that induced by (1. 1) Furthermore it is obvious to see that there occurs no loss of generality if only critical branching processes are considered (compare with [12]) The condition for a branching process to be critical, E = 1, translated into the language of trees is 0 ( and the variance of is given by 2 = 2 00 ( 1.3) Date: December 11, 1996. 1991 Mathematics Subject Classi cation. Primary: 60J80, Secondary: ....
D. P. Kennedy, The Galton-Watson process conditioned on the total progeny, J. Appl. Prob. 12 (1975), 800-806.
Tree-Valued Markov Chains Derived From Galton-Watson Processes. - Aldous, Pitman (1997) (1 citation) (Correct)
....follows that for any particular tree t in which v has n offspring, P (G (h) t j r h G (h) t h ; V h = v) ae Gamma (n)P (G = t j r h G = t h ) 27) for ae Gamma (n) as in (24) Combine (26) and (27) in (25) to obtain (23) for a fixed H = h. 2 Conditioning on the total progeny. Kennedy [24] obtained an analog of the conditioned limit theorem (20) as n 1 with conditioning on #G = n instead of Z n G 0, where #G = P n Z n G is the total progeny. His assumption on the offspring distribution p( Delta) is that the generating function g(s) P n p(n)s n satisfies 9 a 0 with ....
D.P. Kennedy. The Galton-Watson process conditioned on the total progeny. J. Appl. Probab., 12:800--806, 1975.
Stochastic Analysis Of Tree-Like Data Structures - Drmota (2002) (Correct)
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D. P. Kennedy, The Galton-Watson process conditioned on the total progeny, J. Appl. Prob. 12 (1975), 800-806.
Convergence Of Branching Processes To The Local Time Of A.. - Gittenberger (Correct)
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D. P. Kennedy, The Galton-Watson process conditioned on the total progeny, J. Appl. Prob. 12 (1975), 800--806.
The SDE solved by local times of a Brownian excursion or bridge.. - Pitman (1997) (11 citations) (Correct)
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D.P. Kennedy. The Galton-Watson process conditioned on the total progeny. J. Appl. Probab., 12:800--806, 1975.
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