Memory-based persistence in a counting random walk process

Pierre Vallois, Charles S. Tapiero

Research output: Contribution to journalArticlepeer-review


This paper considers a memory-based persistent counting random walk, based on a Markov memory of the last event. This persistent model is a different than the Weiss persistent random walk model however, leading thereby to different results. We point out to some preliminary result, in particular, we provide an explicit expression for the mean and the variance, both nonlinear in time, of the underlying memory-based persistent process and discuss the usefulness to some problems in insurance, finance and risk analysis. The motivation for the paper arose from the counting of events (whether rare or not) in insurance that presume that events are time independent and therefore based on the Poisson distribution for counting these events.

Original languageEnglish (US)
Pages (from-to)303-317
Number of pages15
JournalPhysica A: Statistical Mechanics and its Applications
Issue number1
StatePublished - Dec 1 2007


  • Insurance
  • Markov chains
  • Persistence
  • Random walk

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability


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