TY - JOUR

T1 - Likely path to extinction in simple branching models with large initial population

AU - Klebaner, F. C.

AU - Liptser, R.

PY - 2006

Y1 - 2006

N2 - We give explicit formulae for most likely paths to extinction in simple branching models when initial population is large. In discrete time, we study the Galton-Watson process, and in continuous time, the branching diffusion. The most likely paths are found with the help of the large deviation principle (LDP). We also find asymptotics for the extinction probability, which gives a new expression in continuous time and recovers the known formula in discrete time. Due to the nonnegativity of the processes, the proof of LDP at the point of extinction uses a nonstandard argument of independent interest.

AB - We give explicit formulae for most likely paths to extinction in simple branching models when initial population is large. In discrete time, we study the Galton-Watson process, and in continuous time, the branching diffusion. The most likely paths are found with the help of the large deviation principle (LDP). We also find asymptotics for the extinction probability, which gives a new expression in continuous time and recovers the known formula in discrete time. Due to the nonnegativity of the processes, the proof of LDP at the point of extinction uses a nonstandard argument of independent interest.

UR - http://www.scopus.com/inward/record.url?scp=33745357131&partnerID=8YFLogxK

U2 - 10.1155/JAMSA/2006/60376

DO - 10.1155/JAMSA/2006/60376

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AN - SCOPUS:33745357131

SN - 1048-9533

VL - 2006

JO - Journal of Applied Mathematics and Stochastic Analysis

JF - Journal of Applied Mathematics and Stochastic Analysis

M1 - 60376

ER -