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Displaying 81 –
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209
We consider an age-dependent branching particle system in ℝd,
where the particles are subject to α-stable migration
(0 < α ≤ 2), critical binary branching, and
general (non-arithmetic) lifetimes distribution. The population starts off from a Poisson
random field in ℝd with Lebesgue intensity. We prove
functional central limit theorems and strong laws of large numbers under two rescalings:
high particle density, and a space-time rescaling...
Consider 3-dimensional Brownian motion started on the unit sphere {|x| = 1} with initial density ρ. Let ρt be the first hitting density on the sphere {|x| = t + 1}, t > 0. Then the linear operators Tt defined by Tt ρ = ρt form a semigroup with an infinitesimal generator which is approximately the square root of the Laplacian. This paper studies the analogous situation for Brownian motion with a drift b, where b is small in a suitable scale invariant norm.
The object of this research in the queueing theory is a theorem about the Strong-Law-of-Large-Numbers (SLLN) under the conditions of heavy traffic in a multiserver open queueing network. SLLN is known as a fluid limit or fluid approximation. In this work, we prove that the long-term average rate of growth of the queue length process of a multiserver open queueing network under heavy traffic strongly converges to a particular vector of rates. SLLN is proved for the values of an important probabilistic...
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