TY - JOUR

T1 - POPULATION-SIZE-DEPENDENT BRANCHING PROCESS WITH LINEAR RATE OF GROWTH.

AU - Klebaner, F. C.

PY - 1983/1/1

Y1 - 1983/1/1

N2 - The process we consider is a binary splitting, where the probability of division, p//i equals one-half plus 1/2i, i equals 1,2, . . . , depends on the population size, 2i. We show that Z//n converges to infinity almost surely on set Q OVER BAR of positive probability. Z//n/N converges in distribution to a proper limit, SIGMA ** infinity //n// equals //0(1/Z//n) diverges almost surely on Q OVER BAR , SIGMA ** infinity //n// equals //0(1/Z**2//n) converges almost surely on Q OVER BAR and there are no constants C//n such that Z//n/c//n converges in probability to a non-degenerate limit.

AB - The process we consider is a binary splitting, where the probability of division, p//i equals one-half plus 1/2i, i equals 1,2, . . . , depends on the population size, 2i. We show that Z//n converges to infinity almost surely on set Q OVER BAR of positive probability. Z//n/N converges in distribution to a proper limit, SIGMA ** infinity //n// equals //0(1/Z//n) diverges almost surely on Q OVER BAR , SIGMA ** infinity //n// equals //0(1/Z**2//n) converges almost surely on Q OVER BAR and there are no constants C//n such that Z//n/c//n converges in probability to a non-degenerate limit.

UR - http://www.scopus.com/inward/record.url?scp=0020766915&partnerID=8YFLogxK

U2 - 10.1017/S0021900200023408

DO - 10.1017/S0021900200023408

M3 - Article

AN - SCOPUS:0020766915

VL - 20

SP - 242

EP - 250

JO - Journal of Applied Probability

JF - Journal of Applied Probability

SN - 0021-9002

IS - 2

ER -