Memory-based persistence in a counting random walk process

Pierre Vallois and Charles S. Tapiero

Physica A: Statistical Mechanics and its Applications, 2007, vol. 386, issue 1, 303-317

Abstract: 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.

Keywords: Persistence; Random walk; Insurance; Markov chains (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:386:y:2007:i:1:p:303-317

DOI: 10.1016/j.physa.2007.08.027

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