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
Characterization of spatial Poisson along optional increasing paths---a problem of dimension's reduction / G. Aletti, V. Capasso. - In: STATISTICS & PROBABILITY LETTERS. - ISSN 0167-7152. - 43:4(1999), pp. 343-347.
Characterization of spatial Poisson along optional increasing paths---a problem of dimension's reduction
G. AlettiPrimo
;V. CapassoUltimo
1999
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
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