{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:01:53Z","timestamp":1760144513926,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2024,4,27]],"date-time":"2024-04-27T00:00:00Z","timestamp":1714176000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"FCT-Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia, Portugal","award":["UIDB\/MAT\/04674\/2020"],"award-info":[{"award-number":["UIDB\/MAT\/04674\/2020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics"],"abstract":"<jats:p>In this paper, we investigate the Green measure for a class of non-Gaussian processes in Rd. These measures are associated with the family of generalized grey Brownian motions B\u03b2,\u03b1, 0&lt;\u03b2\u22641, 0&lt;\u03b1\u22642. This family includes both fractional Brownian motion, Brownian motion, and other non-Gaussian processes. We show that the perpetual integral exists with probability 1 for d\u03b1&gt;2 and 1&lt;\u03b1\u22642. The Green measure then generalizes those measures of all these classes.<\/jats:p>","DOI":"10.3390\/math12091334","type":"journal-article","created":{"date-parts":[[2024,4,29]],"date-time":"2024-04-29T04:26:16Z","timestamp":1714364776000},"page":"1334","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Green Measures for a Class of Non-Markov Processes"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4142-0939","authenticated-orcid":false,"given":"Herry P.","family":"Suryawan","sequence":"first","affiliation":[{"name":"Department of Mathematics, Sanata Dharma University, Yogyakarta 55281, Indonesia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5207-1703","authenticated-orcid":false,"given":"Jos\u00e9 L.","family":"da Silva","sequence":"additional","affiliation":[{"name":"CIMA, Faculty of Exact Sciences and Engineering, University of Madeira, Campus da Penteada, 9020-105 Funchal, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2024,4,27]]},"reference":[{"key":"ref_1","unstructured":"Albeverio, S., Fenstad, J.E., Holden, H., and Lindstr\u00f8m, T. 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Stochastic Processes, Physics and Geometry, World Scientific Publishing.","DOI":"10.1142\/9789814541107"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"285003","DOI":"10.1088\/1751-8113\/41\/28\/285003","article-title":"Characterizations and simulations of a class of stochastic processes to model anomalous diffusion","volume":"41","author":"Mura","year":"2008","journal-title":"J. Phys. A Math. Theor."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1080\/10652460802567517","article-title":"A class of self-similar stochastic processes with stationary increments to model anomalous diffusion in physics","volume":"20","author":"Mura","year":"2009","journal-title":"Integral Transform. Spec. 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