{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,3]],"date-time":"2026-02-03T10:22:31Z","timestamp":1770114151563,"version":"3.49.0"},"reference-count":32,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2025,6,24]],"date-time":"2025-06-24T00:00:00Z","timestamp":1750723200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2025,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    The present paper develops a unified approach when dealing with short- or long-range dependent processes with finite or infinite variance. We are concerned with the convergence rate in the strong law of large numbers (SLLN). Our main result is a Marcinkiewicz\u2013Zygmund law of large numbers for\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900225000191_inline1.png\"\/>\n                        <jats:tex-math>$S_{n}(f)= \\sum_{i=1}^{n}f(X_{i})$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    , where\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900225000191_inline2.png\"\/>\n                        <jats:tex-math>$\\{X_i\\}_{i\\geq 1}$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    is a real stationary Gaussian sequence and\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900225000191_inline3.png\"\/>\n                        <jats:tex-math>$f(\\!\\cdot\\!)$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    is a measurable function. Key technical tools in the proofs are new maximal inequalities for partial sums, which may be useful in other problems. Our results are obtained by employing truncation alongside new maximal inequalities. The result can help to differentiate the effects of long memory and heavy tails on the convergence rate for limit theorems.\n                  <\/jats:p>","DOI":"10.1017\/jpr.2025.19","type":"journal-article","created":{"date-parts":[[2025,6,24]],"date-time":"2025-06-24T03:06:43Z","timestamp":1750734403000},"page":"1513-1533","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["Rates for the SLLN for long-memory and heavy-tailed processes"],"prefix":"10.1017","volume":"62","author":[{"given":"Samir","family":"Ben Hariz","sequence":"first","affiliation":[{"name":"Universit\u00e9 du Maine"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7801-4945","authenticated-orcid":false,"given":"Salim","family":"Bouzebda","sequence":"additional","affiliation":[{"name":"Universit\u00e9 de technologie de Compi\u00e8gne"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2025,6,24]]},"reference":[{"key":"S0021900225000191_ref1","doi-asserted-by":"publisher","DOI":"10.1007\/s00362-013-0557-3"},{"key":"S0021900225000191_ref2","doi-asserted-by":"publisher","DOI":"10.1080\/02331888.2018.1425864"},{"key":"S0021900225000191_ref31","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2010.10.011"},{"key":"S0021900225000191_ref28","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176988295"},{"key":"S0021900225000191_ref22","doi-asserted-by":"publisher","DOI":"10.1023\/A:1017588905727"},{"key":"S0021900225000191_ref19","doi-asserted-by":"publisher","DOI":"10.3150\/14-BEJ646"},{"key":"S0021900225000191_ref25","doi-asserted-by":"publisher","DOI":"10.1023\/A:1009985318510"},{"key":"S0021900225000191_ref29","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176988297"},{"key":"S0021900225000191_ref6","unstructured":"[6] Ben Hariz, S. (1999). Limit theorems for weakly and strongly dependent sequences: Statistical applications. 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