{"paper":{"title":"New contributions to the study of stochastic processes of the class $(\\Sigma)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fulgence Eyi Obiang, Octave Moutsinga, Youssef Youssef","submitted_at":"2018-03-27T09:38:48Z","abstract_excerpt":"In this paper, we contribute to the study of the class $(\\Sigma)$. In the first part of the paper, we provide new ways to characterize stochastic processes of the above mentioned class and we derive some new properties. For instance, we prove that a stochastic process $X$ is an element of the class $(\\Sigma)$ if, and only if, its absolute value is equal to absolute value of some martingale $M$. In the second part, we study in particular, stochastic processes of the class $(\\Sigma)$ which vanish on the zero set of a given Brownian motion. More precisely, we provide a characterization theorem an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.09985","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"}