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Cooperative birth processes with linear or sublinear intensity

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  • Küster, Petra

Abstract

Let {Zt} be an increasing Markov process on N n and {[sigma](k)} the corresponding sequence of jump times. Let the increments of Zt be i.i.d. with finite expectation and covariances, and let where h and [latin small letter f with hook] are sufficiently smooth positive functions and [curly logical or]Zt[curly logical or] = [summation operator]nj=1 Zt(j), Zt=(Zt(1),...,Zt(n)). While a linear f results in asymptotically exponential growth, a suitable class of sublinear f leads to a growth asymptotically at most that of a power. Covering both cases, we obtain analoga of the strong LLN, the CLT and LIL.

Suggested Citation

  • Küster, Petra, 1984. "Cooperative birth processes with linear or sublinear intensity," Stochastic Processes and their Applications, Elsevier, vol. 17(2), pages 313-325, July.
    • Handle: RePEc:eee:spapps:v:17:y:1984:i:2:p:313-325
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