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

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.

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Year of publication:	1989
Authors:	Arnold, Barry C. ; Hallett, J. Terry
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 8.1989, 4, p. 377-380
Publisher:	Elsevier
Keywords:	level crossings Pareto processes minimization processes Markov property

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005319144