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Predictable projections for point process filtrations
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  • Published: September 1994

Predictable projections for point process filtrations

  • Günter Last1 

Probability Theory and Related Fields volume 99, pages 361–388 (1994)Cite this article

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Summary

We consider a point process Φ with the Polish phase space (X,X) and a system of σ-fields ℱ(x),x∈X, generated by Φ on certain sets (Γx)∈X. We define predictability for random processes indexed byX and for random measures onX and prove the existence and uniqueness of predictable and dual predictable projections under a regularity condition on Φ. ForX=ℝ +2 and under monotonicity assumptions on the sets Γx we will identify the predictable projections of some simple processes as regular versions of certain martingales.

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Authors and Affiliations

  1. Institut für Mathematische Stochastik, Technische Universität Braunschweig, Postfach 3329, D-38023, Braunschweig, Germany

    Günter Last

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  1. Günter Last
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Last, G. Predictable projections for point process filtrations. Probab. Th. Rel. Fields 99, 361–388 (1994). https://doi.org/10.1007/BF01199897

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  • Received: 09 September 1993

  • Revised: 03 January 1994

  • Issue Date: September 1994

  • DOI: https://doi.org/10.1007/BF01199897

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Mathematics Subject Classification (1991)

  • 60G55
  • 50G57
  • 60G60
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