A problem of reduction of dimension of planar point processes and martingales is faced here by considering these processes along optional increasing paths. Reparametrization of the optional increasing paths by families of ``natural" time preserves the martingale property and makes the process along the path a one-dimensional Poisson process. A novel characterization of spatial martingales and spatial Poisson processes is so obtained.
Reduction of dimension for spatial point processes and right continuous martingales. Characterization of spatial Poisson processes / G. Aletti, V. Capasso. - In: STOCHASTICS AND STOCHASTICS REPORTS. - ISSN 1045-1129. - 72:1-2(2002), pp. 1-9.
Reduction of dimension for spatial point processes and right continuous martingales. Characterization of spatial Poisson processes
G. AlettiPrimo
;V. CapassoUltimo
2002
Abstract
A problem of reduction of dimension of planar point processes and martingales is faced here by considering these processes along optional increasing paths. Reparametrization of the optional increasing paths by families of ``natural" time preserves the martingale property and makes the process along the path a one-dimensional Poisson process. A novel characterization of spatial martingales and spatial Poisson processes is so obtained.
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