J Austral Math Soc Ser A 44 pp71--87, 1988.

Some Limit Theorems for Continuous-State Branching Processes

Anthony G. Pakes

Abstract

The most general continuous time and state branching (C.B.) process (X_t) can be constucted as a certain random time transgormation of a spectrally positive Lévy process. When the generating process is compound Poisson with a superimposed negative linear drift and the C.B. process is not supercritical, then there is a random time T such that X_t+T = e^-ctX_T where c > 0 is the drift parameter. Thus T is the last epoch of random variation. The paper explores a similar phenomenon for the discrete time case and it presents some conditional limit theorems related to the last epoch of random variation. A secondary objective is to present some limit theorems for the C.B. process analagous to known results for the discrete time case.

1980 AMS Subject Classification: 60J80

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Authors

Anthony G. Pakes

Department of Mathematics, University of Western Australia, Nedlands, 6009, Western Australia, Australia.