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A note on explosiveness of Markov branching processes
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- Journal:
- Advances in Applied Probability / Volume 21 / Issue 1 / March 1989
- Published online by Cambridge University Press:
- 01 July 2016, pp. 226-228
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- March 1989
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A note on some results of Schuh
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- Journal:
- Journal of Applied Probability / Volume 21 / Issue 1 / March 1984
- Published online by Cambridge University Press:
- 14 July 2016, pp. 192-196
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- March 1984
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We extend recent results of Schuh on the convergence of
, where α ≧ 0 and Sn is the sum of n i.i.d. positive random variables to sums of the form 
for a large class of functions g, give simpler proofs than those of Schuh, and derive reformulations of the explosion criteria for Markov branching processes with discrete and continuous state space.
, where α ≧ 0 and 
for a large class of functions Sums of i.i.d. random variables and an application to the explosion criterion for markov branching processes
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- Journal:
- Journal of Applied Probability / Volume 19 / Issue 1 / March 1982
- Published online by Cambridge University Press:
- 14 July 2016, pp. 29-38
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- March 1982
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We give necessary and sufficient conditions for
in terms of 
, where Sn is the sum of n i.i.d. random variables with values in]0, ∞[, and A ≧ 0. We use these results to give a probabilistic proof of the ‘explosion criterion' for continuous-time Markov branching processes, which is usually shown analytically.
in terms of 
, where 