Time reversal of some stationary jump diffusion processes from population genetics

Martin Hutzenthaler, Jesse Earl Taylor

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We describe the processes obtained by time reversal of a class of stationary jump diffusion processes that model the dynamics of genetic variation in populations subject to repeated bottlenecks. Assuming that only one lineage survives each bottleneck, the forward process is a diffusion on [0, 1] that jumps to the boundary before diffusing back into the interior. We showthat the behavior of the time-reversed process depends on whether the boundaries are accessible to the diffusive motion of the forward process. If a boundary point is inaccessible to the forward diffusion then time reversal leads to a jump diffusion that jumps immediately into the interior whenever it arrives at that point. If, instead, a boundary point is accessible then the jumps off of that point are governed by a weighted local time of the time-reversed process.

Original languageEnglish (US)
Pages (from-to)1147-1171
Number of pages25
JournalAdvances in Applied Probability
Issue number4
StatePublished - Dec 2010


  • Coalescent
  • Jump diffusion
  • Local time
  • Population bottleneck
  • Selective sweep
  • Time reversal

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics


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