Large jumps of q-Ornstein–Uhlenbeck processes

Yizao Wang

Statistics & Probability Letters, 2016, vol. 118, issue C, 110-116

Abstract: We continue the investigation of sample paths of q-Ornstein–Uhlenbeck processes. We show that for each q∈(−1,1), the process has big jumps crossing from near one end point of the domain to the other with positive probability. Moreover, the number of such jumps in an appropriately enlarged window converges weakly to a Poisson random variable.

Keywords: q-Ornstein–Uhlenbeck process; Markov process; Double-sum method; Poisson limit theorem; Mixing condition; Extreme value theory (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spl.2016.06.025

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