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<article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" article-type="research-article" dtd-version="1.2" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">Доклады Академии наук</journal-id><journal-title-group><journal-title xml:lang="en">Доклады Академии наук</journal-title><trans-title-group xml:lang="ru"><trans-title>Доклады Академии наук</trans-title></trans-title-group></journal-title-group><issn publication-format="print">0869-5652</issn><publisher><publisher-name xml:lang="en">The Russian Academy of Sciences</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="publisher-id">12759</article-id><article-id pub-id-type="doi">10.31857/S0869-56524845523-526</article-id><article-categories><subj-group subj-group-type="toc-heading" xml:lang="en"><subject>Mathematics</subject></subj-group><subj-group subj-group-type="toc-heading" xml:lang="ru"><subject>Математика</subject></subj-group><subj-group subj-group-type="article-type"><subject>Research Article</subject></subj-group></article-categories><title-group><article-title xml:lang="en">A construction of reflecting Lévy processes</article-title><trans-title-group xml:lang="ru"><trans-title>Одна конструкция отражающихся процессов Леви</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Ibragimov</surname><given-names>I. A.</given-names></name><name xml:lang="ru"><surname>Ибрагимов</surname><given-names>И. А.</given-names></name></name-alternatives><address><country country="RU">Russian Federation</country></address><bio xml:lang="en"><p>Academician of the RAS</p></bio><bio xml:lang="ru"><p>Академик РАН</p></bio><email>ibr32@pdmi.ras.ru</email><xref ref-type="aff" rid="aff1"/><xref ref-type="aff" rid="aff2"/></contrib><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Smorodina</surname><given-names>N. V.</given-names></name><name xml:lang="ru"><surname>Смородина</surname><given-names>Н. В.</given-names></name></name-alternatives><address><country country="RU">Russian Federation</country></address><email>smorodina@pdmi.ras.ru</email><xref ref-type="aff" rid="aff1"/><xref ref-type="aff" rid="aff2"/></contrib><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Faddeev</surname><given-names>M. M.</given-names></name><name xml:lang="ru"><surname>Фаддеев</surname><given-names>М. М.</given-names></name></name-alternatives><address><country country="RU">Russian Federation</country></address><email>m.faddeev@spbu.ru</email><xref ref-type="aff" rid="aff1"/><xref ref-type="aff" rid="aff2"/></contrib></contrib-group><aff-alternatives id="aff1"><aff><institution xml:lang="en">Steklov Mathematical Institute of Russian Academy of Sciences at Saint-Peterburg</institution></aff><aff><institution xml:lang="ru">Санкт-Петербургское отделение Математического института им. В.А. Стеклова Российской Академии наук</institution></aff></aff-alternatives><aff-alternatives id="aff2"><aff><institution xml:lang="en">Saint-Petersburg State University</institution></aff><aff><institution xml:lang="ru">Санкт-Петербургский государственный университет</institution></aff></aff-alternatives><pub-date date-type="pub" iso-8601-date="2019-05-16" publication-format="electronic"><day>16</day><month>05</month><year>2019</year></pub-date><volume>484</volume><issue>5</issue><issue-title xml:lang="en"/><issue-title xml:lang="ru"/><fpage>523</fpage><lpage>526</lpage><history><date date-type="received" iso-8601-date="2019-05-21"><day>21</day><month>05</month><year>2019</year></date><date date-type="accepted" iso-8601-date="2019-05-21"><day>21</day><month>05</month><year>2019</year></date></history><permissions><copyright-statement xml:lang="en">Copyright ©; 2019, Russian academy of sciences</copyright-statement><copyright-statement xml:lang="ru">Copyright ©; 2019, Российская академия наук</copyright-statement><copyright-year>2019</copyright-year><copyright-holder xml:lang="en">Russian academy of sciences</copyright-holder><copyright-holder xml:lang="ru">Российская академия наук</copyright-holder></permissions><self-uri xlink:href="https://journals.eco-vector.com/0869-5652/article/view/12759">https://journals.eco-vector.com/0869-5652/article/view/12759</self-uri><abstract xml:lang="en"><p>For some classes of Lévy Processes, the notion of reflection from an interval boundary is introduced. It is shown that trajectories of a reflecting process define random operator that map functions defined on the interval boundaries into elements of <italic>L</italic><sub>2</sub> on the whole interval.</p></abstract><trans-abstract xml:lang="ru"><p>Для некоторых классов одномерных процессов Леви вводится понятие отражения от границы интервала. Показано, что траектории отражающегося процесса определяют случайные операторы, переводящие функции, заданные на границе интервала в элементы <italic>L</italic><sub>2</sub> на всём интервале.</p></trans-abstract><kwd-group xml:lang="en"><kwd>random processes</kwd><kwd>initial boundary value problem</kwd><kwd>limit theorems</kwd><kwd>local time</kwd></kwd-group><kwd-group xml:lang="ru"><kwd>cлучайные процессы</kwd><kwd>начально-краевая задача</kwd><kwd>предельные теоремы</kwd><kwd>локальное время</kwd></kwd-group><funding-group><award-group><award-id></award-id></award-group></funding-group></article-meta></front><body></body><back><ref-list><ref id="B1"><label>1.</label><mixed-citation>Скороход А.В. // Теория вероятностей и ее применения. 1961. Т. 6. № 3. С. 287–298.</mixed-citation></ref><ref id="B2"><label>2.</label><mixed-citation>Pilipenko A. An Introduction to Stochastic Differential Equations with Reflection. 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