{"paper":{"title":"On $\\mathbb{R}^d$-valued multi-self-similar Markov processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Lo\\\"ic Chaumont, Salem Lamine","submitted_at":"2018-09-06T16:43:13Z","abstract_excerpt":"An $\\mathbb{R}^d$-valued Markov process $X^{(x)}_t=(X^{1,x_1}_t,\\dots,X^{d,x_d}_t)$, $t\\ge0,x\\in\\mathbb{R}^d$ is said to be multi-self-similar with index $(\\alpha_1,\\dots,\\alpha_d)\\in[0,\\infty)^d$ if the identity in law \\[(c_iX_t^{i,x_i/c_i};i=1,\\dots,d)_{t\\ge0}\\ed(X_{ct}^{(x)})_{t\\ge0}\\,,\\] where $c=\\prod_{i=1}^dc_i^{\\alpha_i}$, is satisfied for all $c_1,\\dots,c_d>0$ and all starting point $x$. Multi-self-similar Markov processes were introduced by Jacobsen and Yor \\cite{jy} in the aim of extending the Lamperti transformation of positive self-similar Markov processes to $\\mathbb{R}^d_+$-value"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02085","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"}