From the Pseudo-Poisson Processes with the Random Intensity to the Fractional Brownian Motion

Результат исследований: Материалы конференцийматериалы

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Выдержка

We consider a Pseudo-Poisson process, when the leading Poisson
process has a random intensity. Under an appropriate distribution for the random
intensity the corresponding Pseudo-Poisson process possesses a covariance
of the fractional Ornstein-Uhlenbeck process. Applying to the Pseudo-Poisson
processes with the considered random intensity the Lamperti transform and then
the Central Limit Theorem for vectors we obtain the fractional Brownian motion
as a limit in a sense of weak convergence of finite dimensional distributions.
Язык оригиналаанглийский
Страницы161-165
Число страниц5
СостояниеОпубликовано - 2017
СобытиеАналитические и вычислительные методы в теории
вероятностей и её приложениях (АВМТВ-2017) =
Analytical and Computational Methods in Probability
Theory and its Applications (ACMPT-2017)
- МГУ, РУДН, Москва, Российская Федерация
Продолжительность: 23 окт 201727 окт 2017

Конференция

КонференцияАналитические и вычислительные методы в теории
вероятностей и её приложениях (АВМТВ-2017) =
Analytical and Computational Methods in Probability
Theory and its Applications (ACMPT-2017)
Сокращенный заголовокACMPT-2017
СтранаРоссийская Федерация
ГородМосква
Период23/10/1727/10/17

Отпечаток

Fractional Brownian Motion
Poisson process
Fractional
Ornstein-Uhlenbeck Process
Weak Convergence
Central limit theorem
Transform

Ключевые слова

  • Pseudo-Poisson process, Laplace transform, Lamperti transform, fractional Ornstein-Uhlenbeck process, fractional Brownian Motion

Цитировать

Русаков, О. В. (2017). From the Pseudo-Poisson Processes with the Random Intensity to the Fractional Brownian Motion. 161-165. Документ представлен на Аналитические и вычислительные методы в теории
вероятностей и её приложениях (АВМТВ-2017) =
Analytical and Computational Methods in Probability
Theory and its Applications (ACMPT-2017), Москва, Российская Федерация.
Русаков, Олег Витальевич. / From the Pseudo-Poisson Processes with the Random Intensity to the Fractional Brownian Motion. Документ представлен на Аналитические и вычислительные методы в теории
вероятностей и её приложениях (АВМТВ-2017) =
Analytical and Computational Methods in Probability
Theory and its Applications (ACMPT-2017), Москва, Российская Федерация.5 стр.
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abstract = "We consider a Pseudo-Poisson process, when the leading Poissonprocess has a random intensity. Under an appropriate distribution for the randomintensity the corresponding Pseudo-Poisson process possesses a covarianceof the fractional Ornstein-Uhlenbeck process. Applying to the Pseudo-Poissonprocesses with the considered random intensity the Lamperti transform and thenthe Central Limit Theorem for vectors we obtain the fractional Brownian motionas a limit in a sense of weak convergence of finite dimensional distributions.",
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Русаков, ОВ 2017, 'From the Pseudo-Poisson Processes with the Random Intensity to the Fractional Brownian Motion' Документ представлен на Аналитические и вычислительные методы в теории
вероятностей и её приложениях (АВМТВ-2017) =
Analytical and Computational Methods in Probability
Theory and its Applications (ACMPT-2017), Москва, Российская Федерация, 23/10/17 - 27/10/17, стр. 161-165.

From the Pseudo-Poisson Processes with the Random Intensity to the Fractional Brownian Motion. / Русаков, Олег Витальевич.

2017. 161-165 Документ представлен на Аналитические и вычислительные методы в теории
вероятностей и её приложениях (АВМТВ-2017) =
Analytical and Computational Methods in Probability
Theory and its Applications (ACMPT-2017), Москва, Российская Федерация.

Результат исследований: Материалы конференцийматериалы

TY - CONF

T1 - From the Pseudo-Poisson Processes with the Random Intensity to the Fractional Brownian Motion

AU - Русаков, Олег Витальевич

PY - 2017

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N2 - We consider a Pseudo-Poisson process, when the leading Poissonprocess has a random intensity. Under an appropriate distribution for the randomintensity the corresponding Pseudo-Poisson process possesses a covarianceof the fractional Ornstein-Uhlenbeck process. Applying to the Pseudo-Poissonprocesses with the considered random intensity the Lamperti transform and thenthe Central Limit Theorem for vectors we obtain the fractional Brownian motionas a limit in a sense of weak convergence of finite dimensional distributions.

AB - We consider a Pseudo-Poisson process, when the leading Poissonprocess has a random intensity. Under an appropriate distribution for the randomintensity the corresponding Pseudo-Poisson process possesses a covarianceof the fractional Ornstein-Uhlenbeck process. Applying to the Pseudo-Poissonprocesses with the considered random intensity the Lamperti transform and thenthe Central Limit Theorem for vectors we obtain the fractional Brownian motionas a limit in a sense of weak convergence of finite dimensional distributions.

KW - Pseudo-Poisson process, Laplace transform, Lamperti transform, fractional Ornstein-Uhlenbeck process, fractional Brownian Motion

KW - Pseudo-Poisson process, Laplace transform, Lamperti transform, fractional Ornstein-Uhlenbeck process, fractional Brownian Motion

M3 - Paper

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EP - 165

ER -

Русаков ОВ. From the Pseudo-Poisson Processes with the Random Intensity to the Fractional Brownian Motion. 2017. Документ представлен на Аналитические и вычислительные методы в теории
вероятностей и её приложениях (АВМТВ-2017) =
Analytical and Computational Methods in Probability
Theory and its Applications (ACMPT-2017), Москва, Российская Федерация.