Memory-based persistence in a counting random walk process

Pierre Vallois 1, 2 Charles Tapiero 3
INRIA Lorraine, CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, INPL - Institut National Polytechnique de Lorraine, CNRS - Centre National de la Recherche Scientifique : UMR7502
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.
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Pierre Vallois, Charles Tapiero. Memory-based persistence in a counting random walk process. Physica A, Elsevier, 2007, 386 (1), pp.303-317. ⟨10.1016/j.physa.2007.08.027⟩. ⟨hal-00602039⟩



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