Athreya, K.B. (1985) Discounted branching random walks. Adv. Appl. Prob. 17, 53-66. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Diffusion-Limited Aggregation On A Tree - Barlow, Pemantle, Perkins (1994) (1 citation) (Correct)
....H(t) e Gamma(t Gammat n ) for n 1, where t n 1 = h(t n ) and lim n 1 t n = log(d= d Gamma ff) 1 Gamma ff) Gamma1 . Let n 1 in G(t) e t n to complete the proof. Remark. 4.1) and (4.2) are rather nasty equations since they are non linear and (worst of all) anticipative. See Athreya (1985) for some similar equations, arising from the distribution function of the random variable sup x2B T (x) Solutions to these equations are not unique because H j 1 also satisfies (4.1) It is, however, not hard to show that P(T (1) t) is the unique non increasing solution H to (4.1) for which ....
Athreya, K.B. (1985) Discounted branching random walks. Adv. Appl. Prob. 17, 53-66.
Branching Processes - Athreya, Vidyashankar (1999) (113 citations) Self-citation (Athreya) (Correct)
....Biggins [30] also considers uniform convergence of W n ( to W ( for in some compact set. Biggins and Kyprianou [31] consider the Senata constants for BRW. The particular case of BRW, namely the mixed sample case, a point process with i.i.d. components) has been studied by Athreya (see [13]) Asmussen and Kaplan (see [5] 6] and Ney ( 52] In the mixed sample case, if one were to denote by a( E(e Z 1;1 ) then one can see that W n ( reduces to W n ( 1 m n (a( n jZ (n) j X r=1 e zr;n : Recently, Joffe [45] noticed that if one replaces m n by Z n in ....
Athreya,K.B.(1985): Discounted branching random walks, Advances in Applied Probability, 17, N0. 1, 53-66.
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