{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T08:50:24Z","timestamp":1782291024870,"version":"3.54.5"},"reference-count":8,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2026,1,26]],"date-time":"2026-01-26T00:00:00Z","timestamp":1769385600000},"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":[[2026,6]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    A random variable\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" content-type=\"simple\" xlink:href=\"S0021900225100582_inline1.png\">\n                          <jats:alt-text content-type=\"machine-generated\">xi<\/jats:alt-text>\n                        <\/jats:inline-graphic>\n                        <mml:math xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xmlns:mnf=\"http:\/\/cambridge.org\/core\/manifest\" xmlns:cup=\"http:\/\/contentservices.cambridge.org\" xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" xmlns:m=\"http:\/\/cambridge.org\/core\/metadata\" xmlns:core=\"http:\/\/cambridge.org\/core\" xmlns:c=\"http:\/\/cambridge.org\/core\/content\">\n                          <mml:mi>\u03be<\/mml:mi>\n                        <\/mml:math>\n                        <jats:tex-math>$\\xi$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    has a\n                    <jats:italic>light-tailed<\/jats:italic>\n                    distribution (for short, is light-tailed) if it possesses a finite exponential moment,\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" content-type=\"simple\" xlink:href=\"S0021900225100582_inline2.png\">\n                          <jats:alt-text content-type=\"machine-generated\">double struck upper E exp left parenthesis lamda xi right parenthesis less than normal infinity<\/jats:alt-text>\n                        <\/jats:inline-graphic>\n                        <mml:math xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xmlns:mnf=\"http:\/\/cambridge.org\/core\/manifest\" xmlns:cup=\"http:\/\/contentservices.cambridge.org\" xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" xmlns:m=\"http:\/\/cambridge.org\/core\/metadata\" xmlns:core=\"http:\/\/cambridge.org\/core\" xmlns:c=\"http:\/\/cambridge.org\/core\/content\">\n                          <mml:mrow>\n                            <mml:mrow>\n                              <mml:mi mathvariant=\"double-struck\">E<\/mml:mi>\n                            <\/mml:mrow>\n                          <\/mml:mrow>\n                          <mml:mspace width=\"thinmathspace\"\/>\n                          <mml:mrow>\n                            <mml:mi>exp<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:mrow>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>\u03bb<\/mml:mi>\n                            <mml:mi>\u03be<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:mo>&lt;<\/mml:mo>\n                          <mml:mi mathvariant=\"normal\">\u221e<\/mml:mi>\n                        <\/mml:math>\n                        <jats:tex-math>${\\mathbb{E}} \\, {\\exp}{(\\lambda \\xi)} &lt;\\infty$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    for some\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" content-type=\"simple\" xlink:href=\"S0021900225100582_inline3.png\">\n                          <jats:alt-text content-type=\"machine-generated\">lamda greater than 0<\/jats:alt-text>\n                        <\/jats:inline-graphic>\n                        <mml:math xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xmlns:mnf=\"http:\/\/cambridge.org\/core\/manifest\" xmlns:cup=\"http:\/\/contentservices.cambridge.org\" xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" xmlns:m=\"http:\/\/cambridge.org\/core\/metadata\" xmlns:core=\"http:\/\/cambridge.org\/core\" xmlns:c=\"http:\/\/cambridge.org\/core\/content\">\n                          <mml:mi>\u03bb<\/mml:mi>\n                          <mml:mo>&gt;<\/mml:mo>\n                          <mml:mn>0<\/mml:mn>\n                        <\/mml:math>\n                        <jats:tex-math>$\\lambda &gt;0$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    , and has a\n                    <jats:italic>heavy-tailed<\/jats:italic>\n                    distribution (is heavy-tailed) if\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" content-type=\"simple\" xlink:href=\"S0021900225100582_inline4.png\">\n                          <jats:alt-text content-type=\"machine-generated\">double struck upper E exp left parenthesis lamda xi right parenthesis equals normal infinity<\/jats:alt-text>\n                        <\/jats:inline-graphic>\n                        <mml:math xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xmlns:mnf=\"http:\/\/cambridge.org\/core\/manifest\" xmlns:cup=\"http:\/\/contentservices.cambridge.org\" xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" xmlns:m=\"http:\/\/cambridge.org\/core\/metadata\" xmlns:core=\"http:\/\/cambridge.org\/core\" xmlns:c=\"http:\/\/cambridge.org\/core\/content\">\n                          <mml:mrow>\n                            <mml:mrow>\n                              <mml:mi mathvariant=\"double-struck\">E<\/mml:mi>\n                            <\/mml:mrow>\n                          <\/mml:mrow>\n                          <mml:mspace width=\"thinmathspace\"\/>\n                          <mml:mrow>\n                            <mml:mi>exp<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:mrow>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>\u03bb<\/mml:mi>\n                            <mml:mi>\u03be<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:mo>=<\/mml:mo>\n                          <mml:mi mathvariant=\"normal\">\u221e<\/mml:mi>\n                        <\/mml:math>\n                        <jats:tex-math>${\\mathbb{E}} \\, {\\exp}{(\\lambda\\xi)} = \\infty$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    for all\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" content-type=\"simple\" xlink:href=\"S0021900225100582_inline5.png\">\n                          <jats:alt-text content-type=\"machine-generated\">lamda greater than 0<\/jats:alt-text>\n                        <\/jats:inline-graphic>\n                        <mml:math xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xmlns:mnf=\"http:\/\/cambridge.org\/core\/manifest\" xmlns:cup=\"http:\/\/contentservices.cambridge.org\" xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" xmlns:m=\"http:\/\/cambridge.org\/core\/metadata\" xmlns:core=\"http:\/\/cambridge.org\/core\" xmlns:c=\"http:\/\/cambridge.org\/core\/content\">\n                          <mml:mi>\u03bb<\/mml:mi>\n                          <mml:mo>&gt;<\/mml:mo>\n                          <mml:mn>0<\/mml:mn>\n                        <\/mml:math>\n                        <jats:tex-math>$\\lambda&gt;0$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    . Leipus\n                    <jats:italic>et al.<\/jats:italic>\n                    (2023\n                    <jats:italic>AIMS Math.<\/jats:italic>\n                    <jats:bold>8<\/jats:bold>\n                    , 13066\u201313072) presented a particular example of a light-tailed random variable that is the minimum of two independent heavy-tailed random variables. We show that this phenomenon is universal:\n                    <jats:italic>any<\/jats:italic>\n                    light-tailed random variable with right-unbounded support may be represented as the minimum of two independent heavy-tailed random variables. Moreover, a more general fact holds: these two independent random variables may have as heavy-tailed distributions as we wish. Further, we extend the latter result to the minimum of any finite number of independent random variables. We also comment on possible generalizations of our result to the case of dependent random variables.\n                  <\/jats:p>","DOI":"10.1017\/jpr.2025.10058","type":"journal-article","created":{"date-parts":[[2026,1,26]],"date-time":"2026-01-26T11:47:34Z","timestamp":1769428054000},"page":"788-797","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["Any random variable with right-unbounded distributional support is the minimum of independent and very heavy-tailed random variables"],"prefix":"10.1017","volume":"63","author":[{"given":"Anton Sergeevich","family":"Tarasenko","sequence":"first","affiliation":[{"name":"Sobolev Institute of Mathematics"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0116-5846","authenticated-orcid":false,"given":"Sergey","family":"Foss","sequence":"additional","affiliation":[{"name":"Heriot-Watt University and Sobolev Institute of Mathematics"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Georgiy","family":"Krivtsov","sequence":"additional","affiliation":[{"name":"Novosibirsk State University and New Economic School"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2026,1,26]]},"reference":[{"key":"S0021900225100582_ref1","doi-asserted-by":"publisher","DOI":"10.3934\/math.2023658"},{"key":"S0021900225100582_ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2024.129158"},{"key":"S0021900225100582_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-031-34553-1"},{"key":"S0021900225100582_ref5","volume-title":"Comparison Methods for Queues and Other Stochastic Models","author":"Stoyan","year":"1983"},{"key":"S0021900225100582_ref2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-33483-2"},{"key":"S0021900225100582_ref8","volume-title":"An Introduction to Copulas","author":"Nelsen","year":"2006"},{"key":"S0021900225100582_ref7","doi-asserted-by":"publisher","DOI":"10.1007\/s10687-015-0224-2"},{"key":"S0021900225100582_ref3","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-7101-1"}],"container-title":["Journal of Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0021900225100582","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T08:36:33Z","timestamp":1782290193000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0021900225100582\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,26]]},"references-count":8,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,6]]}},"alternative-id":["S0021900225100582"],"URL":"https:\/\/doi.org\/10.1017\/jpr.2025.10058","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"value":"0021-9002","type":"print"},{"value":"1475-6072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,26]]},"assertion":[{"value":"\u00a9 The Author(s), 2026. Published by Cambridge University Press on behalf of Applied Probability Trust","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}]}}