Estimation of the criticality parameter of a superitical branching process with random environments
- 1 June 1979
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 16 (04) , 890-896
- https://doi.org/10.1017/s002190020003357x
Abstract
For a supercritical branching process x = {xn ; n ≧ 0, x 0 = 1} with random environments, define when xn > 0; and = 1 when xn = 0. When x is assumed to satisfy the standard regularity assumptions, under the non-extinction hypothesis, is a strongly consistent and asymptotically unbiased estimator for the criticality parameter π and is asymptotically normal. A strongly consistent estimator, is also proposed for the associated variance, σ 2.Keywords
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