Про стохастичне інтегрування, диференціювання та віківське числення в аналізі білого шуму Леві
The paper is a survey of some author’s results related to the development of the Lévy white noise analysis in terms of Lytvynov’s general- ization of the chaotic representation property, which is an analog of decom- position of square integrable random variables by the Hermite orthogonal polynomials...
Збережено в:
| Дата: | 2022 |
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| Автори та афіліації: |
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| Ключові слова: | keywords |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Українська |
| Опубліковано: |
Інститут математики НАН України
2022
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| Онлайн доступ: | https://trim.imath.kiev.ua/index.php/trim/article/view/496 |
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| Назва журналу: | Transactions of Institute of Mathematics of NAS of Ukraine |
Репозитарії
Transactions of Institute of Mathematics of NAS of Ukraine| Резюме: | The paper is a survey of some author’s results related to the development of the Lévy white noise analysis in terms of Lytvynov’s general- ization of the chaotic representation property, which is an analog of decom- position of square integrable random variables by the Hermite orthogonal polynomials in the Gaussian analysis. Namely with this approach a signifi- cant part of definitions and statements are quite similar to their prototypes from the Gaussian white noise analysis, which is very convenient for possible applications. The survey covers a fairly wide range of issues: constructions of spaces of regular and nonregular test and generalized functions; an extended stochastic integral, a Hida stochastic derivative and operators of stochastic differentiations on different spaces; elements of a Wick calculus; etc. |
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