δ-exceedance records and random adaptive walks

@article{Park2016exceedanceRA,
  title={$\delta$-exceedance records and random adaptive walks},
  author={Su-Chan Park and Joachim H A Krug},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2016},
  volume={49}
}
  • Su-Chan Park, J. Krug
  • Published 16 March 2016
  • Mathematics
  • Journal of Physics A: Mathematical and Theoretical
We study a modified record process where the kth record in a series of independent and identically distributed random variables is defined recursively through the condition Y k > Y k − 1 − δ k − 1 with a deterministic sequence δ k > 0 called the handicap. For constant δ k ≡ δ and exponentially distributed random variables it has been shown in previous work that the process displays a phase transition as a function of δ between a normal phase where the mean record value increases indefinitely… 
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