Cooperative birth processes with linear or sublinear intensity

Petra Küster

Stochastic Processes and their Applications, 1984, vol. 17, issue 2, 313-325

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.

Keywords: birth; process; almost; sure; convergence; multitype; process; central; limit; theorem; cooperation; law; of; iterated; logarithm; exponential; growth; subexponential; growth (search for similar items in EconPapers)
Date: 1984
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