A characterization of the pareto process among stationary stochastic processes of the form Xn = c min(Xn-1, Yn)

Barry C. Arnold and J. Terry Hallett

Statistics & Probability Letters, 1989, vol. 8, issue 4, 377-380

Abstract: Let {Yn} be a sequence of i.i.d. non-negative extended real valued random variables. For c > 0, consider stationary stochastic processes of the form Xn = c min(Xn-1, Yn). Subject to a regularity condition related to the behavior of FYn(y) in a neighborhood of 0, it is verified that the associated level crossing processes, Zn(t) = I(Xn > t), are Markovian for every t if and only if {Xn} is a Pareto process.

Keywords: level; crossings; Pareto; processes; minimization; processes; Markov; property (search for similar items in EconPapers)
Date: 1989
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Citations: View citations in EconPapers (4)

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