Invariance principles for self-similar set-indexed random fields
type: Dataset
description: For a stationary random field $(X_j)_{j\in\Z^d}$ and some measure m on $\R^d$, we consider the set-indexed weighted sum process $S_n(A)=\sum_{j\in\Z^d}m(nA\cap R_j)^\frac12 X_j$, where R_j is the unit cube with lower corner j. We establish a general invariance principle under a p-stability assumption on the X_j's and an entropy condition on the class of sets A. The limit processes are self-similar set-indexed Gaussian processes with continuous sample paths. Using Chentsov's type representations to choose appropriate measures m and particular sets A, we show that these limits can be Lévy (fractional) Brownian fields or (fractional) Brownian sheets.
landing page: 0002-9947
keyword: 60f17-60g60-60g18-60g10-60d05
keyword: chentsovs-type-representation
keyword: dependent-random-field
keyword: infoeu-reposemanticsarticle
keyword: invariance-principle
keyword: journal-articles
keyword: levy-fractional-brownian-field
keyword: mathmath-prmathematics-mathprobability-mathpr
keyword: physical-dependence-measure
keyword: set-indexed-process
keyword: vapnik-chervonenkis-dimension
issued: 2026-05-12T05:13:18.136443
modified: 2026-05-12T05:13:18.136447
language: en
contact point: Organization
  fn: CCSD

test_moissonnage_selune
type: Agent

Invariance principles for self-similar set-indexed random fields
type: Distribution
format: HTML
access URL: https://hal.science/hal-00716437
issued: 2026-05-12T05:13:18.187494
modified: 2026-05-12T05:13:18.120930