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Poisson process via martingale and related characteristics
Published online by Cambridge University Press: 14 July 2016
Abstract
The classical martingale characterizations of the Poisson process were obtained for point process or purely discontinuous martingale i.e. under additional assumptions on properties of trajectories. Here our aim is to search for related characterizations without relying on properties of trajectories. Except for a new martingale characterization, results based on conditional moments jointly involving the past and the nearest future are presented.
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- Copyright © Applied Probability Trust 1999