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Stable transports between stationary random measures

Haji-Mirsadegh, M. O ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1214/16-EJP4237
  3. Publisher: University of Washington
  4. Abstract:
  5. We give an algorithm to construct a translation-invariant transport kernel between two arbitrary ergodic stationary random measures on Rd, given that they have equal intensities.As a result, this yields a construction of a shift-coupling of an arbitrary ergodic stationary random measure and its Palm version.This algorithm constructs the transport kernel in a deterministic manner given a pair of realizations of the two measures.The (non-constructive) existence of such a transport kernel was proved in [9].Our algorithm is a generalization of the work of [3], in which a construction is provided for the Lebesgue measure and an ergodic simple point process.In the general case, we limit ourselves to what we call constrained transport densities and transport kernels.We give a definition of stability of constrained transport densities and introduce our construction algorithm inspired by the Gale-Shapley stable marriage algorithm.For stable constrained transport densities, we study existence, uniqueness, monotonicity w.r.t.the measures and boundedness
  6. Keywords:
  7. Allocation ; Capacity constrained transport kernel ; Mass transport ; Palm distribution ; Shift-coupling ; Stable matching ; Stationary random measure ; Voronoi transport kernel
  8. Source: Electronic Journal of Probability ; Volume 21 , 2016 ; 10836489 (ISSN)
  9. URL: http://projecteuclid.org/euclid.ejp/1470414022