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作者：Ivanoff, B. Gail; Merzbach, Ely
作者单位：University of Ottawa; Bar Ilan University
摘要：We generalize the classic change-point problem to a change-set framework: a spatial Poisson process changes its intensity on an unobservable random set. Optimal detection of the set is defined by maximizing the expected value of a gain function. In the case that the unknown change-set is defined by a locally finite set of incomparable points, we present a sufficient condition for optimal detection of the set using multiparameter martingale techniques. Two examples are discussed.
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作者：Peled, Ron
作者单位：New York University
摘要：Intuitively, two metric spaces are rough isometric (or quasi-isometric) if their large-scale metric structure is the same, ignoring fine details. This concept has proven fundamental in the geometric study of groups. Abert, and later Szegedy and Benjamini, have posed several probabilistic questions concerning this concept. In this article, we consider one of the simplest of these: are two independent Poisson point processes on the line rough isometric almost surely? Szegedy conjectured that the...
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作者：Kella, Offer; Yor, Marc
作者单位：Hebrew University of Jerusalem; Sorbonne Universite; Universite Paris Cite
摘要：We give a representation of the solution for a stochastic linear equation of the form X-t = Y-t + integral((0,t]) X-s-dZ(s) where Z is a cadlag semimartingale and Y is a cadlag adapted process with bounded variation on finite intervals. As an application we study the case where Y and -Z are nondecreasing, jointly have stationary increments and the jumps of -Z are bounded by 1. Special cases of this process are shot-noise processes, growth collapse (additive increase, multiplicative decrease) p...
