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Measure changes with extinction

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  • Harris, S.C.
  • Roberts, M.I.

Abstract

We consider a martingale change of measure and clarify that in general 1/Zt is only a supermartingale under . Defining [Upsilon]:=inf{t>=0:Zt=0} as the extinction time, we then give a necessary and sufficient condition under which the identity holds.

Suggested Citation

  • Harris, S.C. & Roberts, M.I., 2009. "Measure changes with extinction," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1129-1133, April.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:8:p:1129-1133
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    References listed on IDEAS

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    1. Kuhlbusch, Dirk, 2004. "On weighted branching processes in random environment," Stochastic Processes and their Applications, Elsevier, vol. 109(1), pages 113-144, January.
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