{"paper":{"title":"High order chaotic limits of wavelet scalograms under long--range dependence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Ciprian A. Tudor (LPP), Fran\\c{c}ois Roueff (LTCI), Marianne Clausel (LJK), Murad S. Taqqu","submitted_at":"2012-01-23T19:37:52Z","abstract_excerpt":"Let $G$ be a non--linear function of a Gaussian process $\\{X_t\\}_{t\\in\\mathbb{Z}}$ with long--range dependence. The resulting process $\\{G(X_t)\\}_{t\\in\\mathbb{Z}}$ is not Gaussian when $G$ is not linear. We consider random wavelet coefficients associated with $\\{G(X_t)\\}_{t\\in\\mathbb{Z}}$ and the corresponding wavelet scalogram which is the average of squares of wavelet coefficients over locations. We obtain the asymptotic behavior of the scalogram as the number of observations and scales tend to infinity. It is known that when $G$ is a Hermite polynomial of any order, then the limit is either"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4831","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}