Two-parameter Lévy processes: ItÔ formula, semigroups, and generators
We consider random Lévy fields, i.e., stationary fields continuous in probability and having independent increments. We prove that the trajectories of such fields have at most one jump on every line parallel to the axes. We derive an expression for the ItÔ change of variables for Lévy fields. We als...
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| Date: | 1995 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
1995
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5490 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511720744681472 |
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| author | Mishura, Yu. S. Мішура, Ю. С. |
| author_facet | Mishura, Yu. S. Мішура, Ю. С. |
| author_sort | Mishura, Yu. S. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:11:49Z |
| description | We consider random Lévy fields, i.e., stationary fields continuous in probability and having independent increments. We prove that the trajectories of such fields have at most one jump on every line parallel to the axes. We derive an expression for the ItÔ change of variables for Lévy fields. We also consider semigroups generated by Lévy fields and their generators. |
| first_indexed | 2026-03-24T03:17:23Z |
| format | Article |
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| id | umjimathkievua-article-5490 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:17:23Z |
| publishDate | 1995 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/c0/742a07840db1b7f5443511624b6a2ec0.pdf |
| spelling | umjimathkievua-article-54902020-03-19T09:11:49Z Two-parameter Lévy processes: ItÔ formula, semigroups, and generators Двопараметричні процеси: формула Ітo, півгрупи та генератори Mishura, Yu. S. Мішура, Ю. С. We consider random Lévy fields, i.e., stationary fields continuous in probability and having independent increments. We prove that the trajectories of such fields have at most one jump on every line parallel to the axes. We derive an expression for the ItÔ change of variables for Lévy fields. We also consider semigroups generated by Lévy fields and their generators. Розглядаються випадкові поля Леві — стохастично неперервні поля з незалежними приростами. Доведено, що траєкторії такого поля мають не більше одного стрибка на кожній прямій, паралельній осям. Виведено формулу заміни змінних Іто дня полів Леві. Розгляную півгрупи, породжені полями Леві, і а інфінітезімальні оператори цих рун. Institute of Mathematics, NAS of Ukraine 1995-07-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5490 Ukrains’kyi Matematychnyi Zhurnal; Vol. 47 No. 7 (1995); 952–961 Український математичний журнал; Том 47 № 7 (1995); 952–961 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/5490/7669 https://umj.imath.kiev.ua/index.php/umj/article/view/5490/7670 Copyright (c) 1995 Mishura Yu. S. |
| spellingShingle | Mishura, Yu. S. Мішура, Ю. С. Two-parameter Lévy processes: ItÔ formula, semigroups, and generators |
| title | Two-parameter Lévy processes: ItÔ formula, semigroups, and generators |
| title_alt | Двопараметричні процеси: формула Ітo, півгрупи та генератори |
| title_full | Two-parameter Lévy processes: ItÔ formula, semigroups, and generators |
| title_fullStr | Two-parameter Lévy processes: ItÔ formula, semigroups, and generators |
| title_full_unstemmed | Two-parameter Lévy processes: ItÔ formula, semigroups, and generators |
| title_short | Two-parameter Lévy processes: ItÔ formula, semigroups, and generators |
| title_sort | two-parameter lévy processes: itô formula, semigroups, and generators |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5490 |
| work_keys_str_mv | AT mishurayus twoparameterlevyprocessesitoformulasemigroupsandgenerators AT míšuraûs twoparameterlevyprocessesitoformulasemigroupsandgenerators AT mishurayus dvoparametričníprocesiformulaítopívgrupitageneratori AT míšuraûs dvoparametričníprocesiformulaítopívgrupitageneratori |