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Random locations of periodic stationary processes

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  • Shen, Jie
  • Shen, Yi
  • Wang, Ruodu

Abstract

We consider a family of random locations, called intrinsic location functionals, of periodic stationary processes. This family includes but is not limited to the location of the path supremum and first/last hitting times. We first show that the set of all possible distributions of intrinsic location functionals for periodic stationary processes is the convex hull generated by a specific group of distributions. We then focus on two special subclasses of these random locations. For the first subclass, the density has a uniform lower bound; for the second subclass, the possible distributions are closely related to the concept of joint mixability.

Suggested Citation

  • Shen, Jie & Shen, Yi & Wang, Ruodu, 2019. "Random locations of periodic stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 129(3), pages 878-901.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:3:p:878-901
    DOI: 10.1016/j.spa.2018.03.023
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    References listed on IDEAS

    as
    1. Shen, Yi, 2016. "Random locations, ordered random sets and stationarity," Stochastic Processes and their Applications, Elsevier, vol. 126(3), pages 906-929.
    2. Ruodu Wang & Liang Peng & Jingping Yang, 2013. "Bounds for the sum of dependent risks and worst Value-at-Risk with monotone marginal densities," Finance and Stochastics, Springer, vol. 17(2), pages 395-417, April.
    3. Paul Embrechts & Bin Wang & Ruodu Wang, 2015. "Aggregation-robustness and model uncertainty of regulatory risk measures," Finance and Stochastics, Springer, vol. 19(4), pages 763-790, October.
    Full references (including those not matched with items on IDEAS)

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