An invariance result for Hammersley’s process with sources and sinks
نویسنده
چکیده
Let P1 be a Poisson process of intensity λ1 on the positive x-axis, P2 a Poisson process of intensity λ2 on the positive y-axis, and P a Poisson process of intensity λ1λ2 in the interior of IR +, where P1, P2 and P are independent. Then the extended Hammersley process Lλ1(·, t) with sources and sinks given by P1 and P2, respectively, is distributed as a Poisson point process with intensity λ1 for all t ≥ 0. 1 The invariance result Let ξ denote a point process on [0, 1]. That is, ξ is a random (Radon) measure on [0, 1], with realizations of the form ξ(f) def = ∫ 1
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