Stochastic Equations and Equations for Probabilistic Characteristics of Processes with Damped Jumps
Электронный научный архив УРФУ
Информация об архиве | Просмотр оригинала| Поле | Значение | |
| Заглавие |
Stochastic Equations and Equations for Probabilistic Characteristics of Processes with Damped Jumps
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| Автор |
Melnikova, I. V.
Bovkun, V. A. |
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| Тематика |
GENERALIZED FUNCTIONS
PROBABILISTIC CHARACTERISTICS SHOT NOISE STOCHASTIC DIFFERENTIAL EQUATION WIENER PROCESS |
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| Описание |
Processes such as shot noise are an adequate tool for modeling discontinuous random processes with a damping effect. Such processes arise in various fields of physics, technology and human activity, including the field of finance. They allow to simulate not only abrupt changes in the values of processes with jumps, but also the subsequent return of values to their original or near the original position. For this reason, shot noise is a suitable tool for simulating price hikes of various market assets. This paper presents a general formulation of the shot noise type processes, a stochastic differential equation corresponding to the process, and a connection with the integral-differential equation for the transition probability density, which is formulated in terms of generalized functions. In addition, the paper considers a stochastic equation that allows, along with an abrupt change described by a process of the shot noise type, a continuous change in the process. An equation is obtained for the transition probability density of a process containing jump-like and continuous types of evolution, which should also be considered in spaces of generalized functions. Thus, main results of the paper are obtained on the basis of the application of stochastic analysis and the theory of generalized functions. © 2023 Irkutsk State University. All rights reserved.
Russian Science Foundation, RSF: 23–21–00199 This work was supported by Russian Science Foundation, project This work was supported by Russian Science Foundation, project No. 23–21–00199. |
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| Дата |
2024-04-05T16:34:51Z
2024-04-05T16:34:51Z 2023 |
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| Тип |
Article
Journal article (info:eu-repo/semantics/article) |info:eu-repo/semantics/publishedVersion |
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| Идентификатор |
Мельникова, ИВ & Бовкун, ВА 2023, 'Стохастические уравнения и уравнения для вероятностных характеристик процессов с затухающими скачками', Известия Иркутского государственного университета. Серия: Математика, Том. 45, стр. 73-88. https://doi.org/10.26516/1997-7670.2023.45.73
Мельникова, И. В., & Бовкун, В. А. (2023). Стохастические уравнения и уравнения для вероятностных характеристик процессов с затухающими скачками. Известия Иркутского государственного университета. Серия: Математика, 45, 73-88. https://doi.org/10.26516/1997-7670.2023.45.73 1997-7670 Final All Open Access, Gold https://www.scopus.com/inward/record.uri?eid=2-s2.0-85174930852&doi=10.26516%2f1997-7670.2023.45.73&partnerID=40&md5=aed4a44a45561b9801cefc643aa7149d https://doi.org/10.26516/1997-7670.2023.45.73 http://elar.urfu.ru/handle/10995/130880 54482996 10.26516/1997-7670.2023.45.73 85174930852 001071184700004 |
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| Язык |
ru
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| Связанные ресурсы |
info:eu-repo/grantAgreement/RSF//23-21-00199
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| Права |
Open access (info:eu-repo/semantics/openAccess)
cc-by-nc https://creativecommons.org/licenses/by-nc/4.0/ |
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| Формат |
application/pdf
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| Издатель |
Irkutsk State University
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| Источник |
The Bulletin of Irkutsk State University. Series Mathematics
Bulletin of Irkutsk State University, Series Mathematics |
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