Stable transports between stationary random measures
| Autor: | Mir-Omid Haji-Mirsadeghi, Ali Khezeli |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Statistics and Probability
stable matching Stability (probability) Point process allocation shift-coupling FOS: Mathematics Applied mathematics Ergodic theory Uniqueness stationary random measure Mathematics capacity constrained transport kernel Lebesgue measure Probability (math.PR) palm distribution mass transport Voronoi transport kernel Stable marriage problem Random measure Kernel (statistics) 60G57 60G57 60G55 60G10 60G55 Statistics Probability and Uncertainty 60G10 Mathematics - Probability |
| Zdroj: | Electron. J. Probab. |
| ISSN: | 1083-6489 |
| DOI: | 10.1214/16-ejp4237 |
| Popis: | We give an algorithm to construct a translation-invariant transport kernel between ergodic stationary random measures $\Phi$ and $\Psi$ on $\mathbb R^d$, given that they have equal intensities. As a result, this yields a construction of a shift-coupling of an ergodic stationary random measure and its Palm version. This algorithm constructs the transport kernel in a deterministic manner given realizations $\varphi$ and $\psi$ of the measures. The (non-constructive) existence of such a transport kernel was proved in [8]. 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 densities and transport kernels. We give a definition of stability of constrained densities and introduce our construction algorithm inspired by the Gale-Shapley stable marriage algorithm. For stable constrained densities, we study existence, uniqueness, monotonicity w.r.t. the measures and boundedness. Comment: In the second version, we change the way of presentation of the main results in Section 4. The main results and their proofs are not changed significantly. We add Section 3 and Subsection 4.6. 25 pages and 2 figures |
| Databáze: | OpenAIRE |
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