Record Statistics of Integrated Random Walks and the Random Acceleration Process

  title={Record Statistics of Integrated Random Walks and the Random Acceleration Process},
  author={Claude Godr{\`e}che and Jean-Marc Luck},
  journal={Journal of Statistical Physics},
  • C. Godrèche, J. Luck
  • Published 12 September 2021
  • Physics, Mathematics
  • Journal of Statistical Physics
We address the theory of records for integrated random walks with finite variance. The long-time continuum limit of these walks is a non-Markov process known as the random acceleration process or the integral of Brownian motion. In this limit, the renewal structure of the record process is the cornerstone for the analysis of its statistics. We thus obtain the analytical expressions of several characteristics of the process, notably the distribution of the total duration of record runs… 

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