Heyde,C.C.(1970): Extension of a result of Seneta for supercritical GaltonWatson Processes, Annals of Mathematical Statistics, 41, 739-742. Home/Search Document Not in Database Summary Related Articles Check |
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Branching Processes - Athreya, Vidyashankar (1999) (113 citations) (Correct)
....that c Gamma1 n c n 1 m and c Gamma1 n Z n converges with probability 1 (w.p.1) to a finite random variable W that is nontrivial, is, P (W = 0jZ 0 = 1) q 1. The constants c n are called Senata Heyde constants and the result was first established by Senata [55] and strengthened by Heyde [39]. Athreya [15] showed that if fZ n : n 1g and fZ 0 n : n 1gare two independent copies of branching processes, then Z Gamma1 n Z 0 n converges to a random variable W and if m 1 then P (0 W 1) 1;however if m = 1 then P (W = 0) and P (W = 1) are both positive. This says that in the ....
Heyde,C.C.(1970): Extension of a result of Seneta for supercritical GaltonWatson Processes, Annals of Mathematical Statistics, 41, 739-742.
Estimation Of The Parameters Of A Branching Process From.. - Jacob, Peccoud (1998) (Correct)
.... results concerning the asymptotic behaviour, as n 1, of the classical estimators based on the BGW process, b mn = P n 1 N k ) P n Gamma1 0 N k ) Gamma1 , mn = N n (N n Gamma1 ) Gamma1 and oe 2 n 1 = n Gamma1 P n k=1 (N k 1 Gamma mn 1N k ) 2 (N k ) Gamma1 (Heyde [18], 19] 22] Heyde and Leslie [23] Athreya and Ney [2] Basawa and Scott [3] Hall and Heyde [16] Guttorp [15] The convergence of the normalized observed process to the variable WN0 ;fF n gn , limit of the normalized branching process N n , is derived using the classical results of ....
Heyde, C.C. (1970) Extension of a result of Seneta for the super-critical GaltonWatson process. Ann. Math. Statist. 41, 739--742.
Probabilit'es, Statistiques - Estimation De (Correct)
....2 ZnN a une immigration. Lorsque ffi = 0 et p vn = 1, pour tout n, le processus fN n;vn g n est r eduit a un simple processus de Galton Watson g en er e par F et not e fN n g n . Le comportement asymptotique d un tel processus ainsi que les propri et es des estimateurs de m sont connus (Heyde [8], 9] Heyde Leslie [10] Athreya Ney [1] Hall Heyde [7] Guttorp [6] Dans le cas g en eral, fN n;vn g n correctement normalis e n est plus une martingale. On g en eralise ici les r esultats relatifs au cas simple. On montre que f Nn;vn pvn p Vn g n converge p.s. et dans L 2 vers la ....
....Zn N to an immigration. When ffi = 0 and p vn = 1, for all n, process fN n;vn g n is reduced to a simple supercritical Galton Watson process generated by F and denoted by fN n g n . The asymptotic behaviour of such a process as well as the properties of the estimators of m are well known (Heyde [8], 9] Heyde Leslie [10] Athreya Ney [1] Hall Heyde [7] Guttorp [6] fN n;vn g n correctly normalized is, generally, no longer a martingale. We extend here the results relative to the simple case. Let F n be the oe algebra generated by fN k;V k ; N k;v k g kn , p Vn = Pi n Gamma1 k=1 ....
C.C. Heyde (1970) Extension of a result of Seneta for the super-critical Galton-Watson process. Ann. Math. Statist. 41, 739-742.
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