{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,1]],"date-time":"2025-12-01T06:39:32Z","timestamp":1764571172369,"version":"build-2065373602"},"reference-count":21,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2024,9,8]],"date-time":"2024-09-08T00:00:00Z","timestamp":1725753600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"PIP-GI-CONICET \u201cEfectos de viento, explosiones y fuego en tanques de almacenamiento de combustibles\u201d"},{"name":"Proyecto Consolidar, SECyT-Universidad Nacional de C\u00f3rdoba \u201cDesarrollo y aplicaci\u00f3n de estudios te\u00f3ricos, num\u00e9ricos y c\u00f3digos computacionales en mec\u00e1nica de fluidos e intermitencia ca\u00f3tica\u201d"},{"name":"Facultad de Ingenier\u00eda y Ciencias B\u00e1sicas, Fundaci\u00f3n Universitaria los Libertadores, CNRS and University Pau and Pays Adour, LMAP, Inria Cagire Team"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Many physical processes feature random telegraph signals, e.g., a time signal c(t) that randomly switches between two values over time. The present study focuses on the class of telegraphic processes for which the transition rates are formulated by using fractal-like expressions. By considering various restrictive hypotheses regarding the statistics of the waiting times, the present analysis provides the corresponding expressions of the unconditional and conditional probabilities, the mean waiting times, the mean phase duration, the autocorrelation function and the associated integral time scale, the spectral density, and the mean switching frequency. To assess the relevance of the various hypotheses, synthetically generated signals were constructed and used as references to evaluate the predictive quality of the theoretically derived expressions. The best predictions were obtained by considering that the waiting times probability density functions were Dirac peaks centered on the corresponding mean values.<\/jats:p>","DOI":"10.3390\/sym16091175","type":"journal-article","created":{"date-parts":[[2024,9,9]],"date-time":"2024-09-09T03:04:18Z","timestamp":1725851058000},"page":"1175","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Random Telegraphic Signals with Fractal-like Probability Transition Rates"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7250-0392","authenticated-orcid":false,"given":"Sergio","family":"Elaskar","sequence":"first","affiliation":[{"name":"Departamento de Aeron\u00e1utica, FCEFyN e Instituto de Estudios Avanzados en Ingenier\u00eda y Tecnolog\u00eda (IDIT), Universidad Nacional de C\u00f3rdoba and CONICET, C\u00f3rdoba 5000, Argentina"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5335-7869","authenticated-orcid":false,"given":"Pascal","family":"Bruel","sequence":"additional","affiliation":[{"name":"Centre National de la Recherche Scientifique (CNRS), Laboratoire de Math\u00e9matiques et de Leurs Applications (LMAP), Inria Cagire Team, Universit\u00e9 de Pau et des Pays de l\u2019Adour (UPPA), 64013 Pau, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2035-7640","authenticated-orcid":false,"given":"Luis","family":"Guti\u00e9rrez Marcantoni","sequence":"additional","affiliation":[{"name":"Facultad de Ingenier\u00eda y Ciencias B\u00e1sicas, Fundaci\u00f3n Universitaria Los Libertadores, Bogot\u00e1 110441, Colombia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,9,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1007\/BF02368011","article-title":"The fractal random telegraphic signal: Signal analysis and applications","volume":"16","author":"Liebovitch","year":"1988","journal-title":"Ann. 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