A result like the Kesten-Stigum theorem is obtained for certain martingales associated with
the branching random walk. A special case, when a 'Malthusian parameter'exists, is …

We consider a generalized Mandelbrot's martingale {Yn} and the associated Mandelbrot's
measure μω on marked trees. If the limit variable Z= lim Y n is not degenerate, we study the …

We obtain results connecting the distributions of the random variables Z1 and W in the
supercritical Galton-Watson process. For example, if a> 1, and converge or diverge together …

Let {Ai: i≥ 1} be a sequence of non-negative random variables and let M be the class of all
probability measures on [0,∞]. Define a transformation T on M by letting Tμ be the …

The present book offers a detailed treatment of perturbed random walks, perpetuities, and
random processes with immigration. These objects are of major importance in modern …

Queueing theory occupies a prominent role in the performance analysis of a wide range of
systems in computer-communications, logistics, and manufacturing. One of the pillars of …

We study properties of stable-like laws, which are solutions of the distributional equation Z=
d∑ i= 1NA iZ i, where (N, A1, A2,…) is a given random variable with values in {0 …

Abstract Let A=(A_1,A_2,A_3,...) be a random sequence of non-negative numbers that are
ultimately zero with E∑A_i=1 and E\left∑A_i\logA_i\right≦0. The uniqueness of the non …

We show for the M/G/1 processor sharing queue that the service time distribution is regularly
varying of index-ν, ν non-integer, iff the sojourn time distribution is regularly varying of index …

N.II.BINGHAM We consider the random time-change connecting continuous-time continuous-state
branching processes (CB-processes) w Page 1 Stochastic Processes and Their Applications …