Characterization of spatial Poisson along optional increasing paths: A problem of dimension's reduction

G. Aletti and V. Capasso

Statistics & Probability Letters, 1999, vol. 43, issue 4, 343-347

Abstract: A problem of reduction of dimension of a plane Poisson process is faced here by considering this process along optional increasing paths. A suitable reparametrization of an optional increasing path makes the process along the path a one-parameter Poisson process. A convenient characterization of the spatial Poisson process is so obtained. The key idea developed in this paper relates to the corresponding result which holds for one-parameter martingales stopped by a bounded stopping time.

Keywords: Martingales; Poisson; process; Optional; increasing; path (search for similar items in EconPapers)
Date: 1999
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