Random locations of periodic stationary processes
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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.
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Jie Shen, Yi Shen, Ruodo Wang (2019). Random locations of periodic stationary processes. UWSpace. http://hdl.handle.net/10012/15404
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