K.B. Athreya, Some results on multitype continuous time Markov branching processes. Ann. Math. Statist. 39 (1968), 347--357. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Functional Limit Theorems For Multitype Branching Processes And.. - Janson (Correct)
....and with Re# 2 # 1 , we have in (3.19) by Corollary 3.23 with b : m 1 a and (3.17) EV (x)V (y) # = mx# I (y x) m 1 A # 6. Relations to previously known results Large parts of Theorem 3.1 are known since Athreya s thesis, at least in the irreducible case: the a.s. convergence is in [4] and [9, Theorem V.7.2] and the limits in Corollary 3.8 are proved in [5] 6] see also [9, V.8] Our results give more explicit formulas for the asymptotic variances and covariances, and the extension to stochastic processes. The independence between the limit processes in (i) and (ii) seems ....
....branching process, and by [9, Theorem V.7.2] W = 0 a.s. implies extinction, t) 0 for large t, and thus u 1 = 0 for large t. The result follows. # We may further improve this result to the first claim in Theorem 3.1. a.s. Wv 1 . Proof. This is Theorem V.7. 2 in [9] see also [4], but since our setting is somewhat more general, we give a complete proof. Fix an eigenvalue # # 1 and let # : # 1 Re# 0. Let # 0 and let n be the event sup t#[n 1,n] #. If n occurs, then, by (2.10) for some t [n 1, n] #e (t) Cn t(# ....
K.B. Athreya, Some results on multitype continuous time Markov branching processes. Ann. Math. Statist. 39 (1968), 347--357.
Branching Processes - Athreya, Vidyashankar (1999) (113 citations) Self-citation (Athreya) (Correct)
....probability. It follows from the above theorem that, under a finite mean assumption on the offspring distribution function, Z Gamma1 n Z n 1 converges to m( 1) as n 1 w.p.1 on the set of explosion. A central limit theorem for the sequence f Zn 1 Zn ; n 1g is given below (see Athreya [9] and Heyde [40] Theorem 3. Assume p 0 = 0 and E(Z 2 ffi 1 ) 1. Then q Z n ( Z n 1 Z n Gamma m) d N(0; oe 2 ) where N(0; oe 2 ) is a normal random variable with mean 0 and variance oe 2 . 2 A law of iterated logarithm associated with the above convergence has been established ....
Athreya,K.B.(1968): Some results on multitype continuous time Markov branching processes, Annals of Mathematical Statistics, 20, 649-651.
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC