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Let the martingale W n = Zn m n , where Z n is a weighted branching process and m = E i T i is the expected sum of the = factors T i , converge to some limiting random variable W. We give conditions in terms of the factors such that W belongs to the domain of attraction or to the domain of normal attraction of an = α–stable distribution with 1 < α ≤ 2.… (More)

A continuous time branching random walk on the lattice is considered in which individuals may produce children at the origin only. Assuming that the underlying random walk is symmetric and the offspring reproduction law is critical we prove a conditional limit theorem for the number of individuals at the origin. 1 Statement of problem and main results We… (More)

—It is known that in many queueing systems fluid limits are deterministic functions. Models and conditions which lead to random fluid limits have not received much attention. This paper is devoted to a study of a queueing network whose fluid limits admit a random and uncountable branching at certain points. Stability conditions for this model are… (More)

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