J. D. Biggins (1992). Uniform convergence of martingales in the branching random walk Ann. Probab. 20, 137-151. Home/Search Document Not in Database Summary Related Articles Check |
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....X which is charact#jTT: by afunct#FjTT equat##Fj The surprise ,not so unexp aft#pF ards, ist#F# t#F# are phase changes in t#Flimit law, depending on t#F asympt#Fj: behaviour of p. Here andlat# we regard n and p as independent variables. In t#F limit result# we always assume n ##and [0, 1],oft#O wit# furt# : condit#EFj added. ALONS#4 CHAS#40.67 GILLET, JANS#T, REINGOLD S#3965 Theorganizat#HO oft#F# paper is as follows: Theresult# arest#F : inSect#:H 2. InSect# 0 3, we est#O EFj a generalfunct#F#I equat##F for I(n, p) In t#F remaining sect#ning we prove convergence result# for ....
....inSect# # 5 , for t#r first t wo cases. These met#e ds donot apply for Case 3, which requires poissonizat#IH (seeSect# T 6, where we use an embedding of Quicksort in a Poisson point process) 2. Results X n,p = We will alwayslet Udenot# a random variablet#ia is uniformlydist#mlyFOT on [0, 1]. Also, # shall denot# t#n set of posit#H e int# #O0 Nt# set ofnonnegat#O e int#FT O: Case 1: lim p = c 0. Theorem 2.1. If lim p = c, c #]0, 1] X ,p ges indistr#9:A682 to ar andom var#m:88 X c whose distr#3736:A ischar acter#83 d as the unique solution with finite mean of the equation ....
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J.D. Biggins. Uniform convergence of martingales in the branching random walk, Ann. Probab., 20(1):137--151, 1992.
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....1 ( log W 1 ( jZ (0) ffi 0 ) 1 or 1: 2 The details of proof can be found in Biggins (see [28 ] where the assumption m( 1 for all is considerably reduced. A conceptual proof of the above result along the lines of the one in [49] has been established by Lyons (see [50] 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 ....
Biggins,J.D.(1992): Uniform convergence of martingales in the branching random walk, Annals of Probability, 20, No. 1, 137-151.
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Biggins, J.D. (1992). Uniform convergence of martingales in the branching random walk. Ann. Probab. 20, 137-151.
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Biggins, J.D. (1992). Uniform convergence of martingales in the branching random walk. Ann. Probab. 20, 137--151.
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Biggins, J.D. (1992). Uniform convergence of martingales in the branching random walk. Ann. Probab. 20, 137--151.
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Biggins, J.D. (l989). Uniform convergence of martingales in the branching random walk. (submitted to Ann. Probab.)
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Biggins, J.D. (1992). Uniform convergence of martingales in the branching random walk. Ann. Probab. 20, 137--151.
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J. D. Biggins (1992). Uniform convergence of martingales in the branching random walk Ann. Probab. 20, 137-151.
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J.D. Biggins. Uniform convergence of martingales in the branching random walk, Ann. Probab., 20(1):137-151, 1992.
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Biggins, J.D. (1992) Uniform convergence of martingales in the branching random walk. Ann. Probab 20 137--151
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