New PDF release: Branching Processes: Proceedings of the First World Congress

By Harry Cohn (auth.), C. C. Heyde (eds.)

ISBN-10: 0387979891

ISBN-13: 9780387979892

ISBN-10: 1461225582

ISBN-13: 9781461225584

This quantity provides the edited court cases of the 1st international Congress on Branching procedures. The contributions current new examine and surveys of the present examine task during this box. accordingly, all these venture learn within the topic will locate this a well timed and fine quality quantity to have on their cabinets.

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Get Branching Processes: Proceedings of the First World Congress PDF

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All offspring are born at 0, the initial time moment. After that all conditions of Theorem 2 are true for a new process and L(t) is the same in both cases and it was used in the introduction. Condition (3) extends the condition E(t) = o(L(t)). " are independent and q(t,y) '" q(t), as t --+ 00, and L(t) may be defined by the equation G(L(t)) = q(t), or equivalently L(t) = G_1(q(t)). Then A(t) '" J~ tdF(t) and it follows from Theorem 2 that: Corollary l. Let Z(t) be a critical Bellman-Harris process, q(t) E £ and the condition l udq(u)G_1(q(t))q-l(t) = o(t), holds, as t --+ 00.

S. v. Some results for the processes with == 0 and It == I? s. were announced by Yaney and Yanev(1991). e. p = Pt, q = qt and r = rt were investigated by Yaney and Mitov(1985). An important characteristic of the process {tt} is the life-period T = T(T) started at the moment T 2: 0, and defined by YT-l = 0, YT+n > 0, 0 :::; n < T, YT+ T = O. Further on we will also consider the process stopped at zero {Zt} defined by :"'It "'It "'It Zt d = YT+tI{Zt_l > O}' t "'It = 1,2, ... e. P(YT = n) = P(If = n IIf> 0), n 2: 1.

Heyde for the great edit help 29 All properties of Markov processes Z(t) (N and I} are independent, N(t) = 0, for I} < t, and I} = 1, or I} is exponentially distributed) are described in terms of a generating function for N and its iterations. Properties of Bellman-Harris processes Z(t) ( Nand I} are independent, N(t) = 0, for I} < t, and I} is arbitrary distributed) are essentially dependent on generating function for Nand q( t) = P {I} > t}. Properties of general processes Z(t) are essentially dependent on A(t) in addition to the last two parametric families, where A(t) = max{l,E{I:~l a(i); I} :S t }}, if A(t) -+ 00 for t -+ 00, or A(t) = EI:~1 a(i) = a otherwise.

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Branching Processes: Proceedings of the First World Congress by Harry Cohn (auth.), C. C. Heyde (eds.)


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