{"paper":{"title":"Spectral Analysis of Multi-dimensional Self-similar Markov Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.PR","authors_text":"N. Modarresi, S. Rezakhah","submitted_at":"2009-07-14T07:11:33Z","abstract_excerpt":"In this paper we consider a discrete scale invariant (DSI) process $\\{X(t), t\\in {\\bf R^+}\\}$ with scale $l>1$. We consider to have some fix number of observations in every scale, say $T$, and to get our samples at discrete points $\\alpha^k, k\\in {\\bf W}$ where $\\alpha$ is obtained by the equality $l=\\alpha^T$ and ${\\bf W}=\\{0, 1,...\\}$. So we provide a discrete time scale invariant (DT-SI) process $X(\\cdot)$ with parameter space $\\{\\alpha^k, k\\in {\\bf W}\\}$. We find the spectral representation of the covariance function of such DT-SI process. By providing harmonic like representation of multi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.2295","kind":"arxiv","version":4},"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"}