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Decidable lim sup and Borel–Cantelli-like lemmas for random sequences


  • Davie, George


We prove computable versions of limsup events and Borel–Cantelli-like results for algorithmically random sequences using a coefficient from Kolmogorov complexity. In particular we show that under suitable conditions on events, limsup is layerwise decidable.

Suggested Citation

  • Davie, George, 2013. "Decidable lim sup and Borel–Cantelli-like lemmas for random sequences," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 278-285.
  • Handle: RePEc:eee:stapro:v:83:y:2013:i:1:p:278-285 DOI: 10.1016/j.spl.2012.09.010

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    References listed on IDEAS

    1. Abundo, Mario, 2002. "Some conditional crossing results of Brownian motion over a piecewise-linear boundary," Statistics & Probability Letters, Elsevier, vol. 58(2), pages 131-145, June.
    2. Abundo, Mario, 2012. "An inverse first-passage problem for one-dimensional diffusions with random starting point," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 7-14.
    3. Jackson, Ken & Kreinin, Alexander & Zhang, Wanhe, 2009. "Randomization in the first hitting time problem," Statistics & Probability Letters, Elsevier, vol. 79(23), pages 2422-2428, December.
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