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

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  • Aletti, G.
  • Capasso, V.

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.

Suggested Citation

  • Aletti, G. & Capasso, V., 1999. "Characterization of spatial Poisson along optional increasing paths: A problem of dimension's reduction," Statistics & Probability Letters, Elsevier, vol. 43(4), pages 343-347, July.
    • Handle: RePEc:eee:stapro:v:43:y:1999:i:4:p:343-347
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