{"paper":{"title":"Symmetric stochastic integrals with respect to a class of self-similar Gaussian processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Arturo Jaramillo, Daniel Harnett, David Nualart","submitted_at":"2017-06-13T02:19:45Z","abstract_excerpt":"We study the asymptotic behavior of the $\\nu$-symmetric Riemman sums for functionals of a self-similar centered Gaussian process $X$ with increment exponent $0<\\alpha<1$. We prove that, under mild assumptions on the covariance of $X$, the law of the weak $\\nu$-symmetric Riemman sums converge in the Skorohod topology when $\\alpha=(2\\ell+1)^{-1}$, where $\\ell$ denotes the smallest positive integer satisfying $\\int_{0}^{1}x^{2j}\\nu(dx)=(2j+1)^{-1}$ for all $j=0,\\dots, \\ell-1$. In the case $\\alpha>(2\\ell+1)^{-1}$, we prove that the convergence holds in probability."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.03890","kind":"arxiv","version":1},"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"}