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

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From the Pseudo-Poisson Processes with the Random Intensity to the Fractional Brownian Motion. / Rusakov, O. V. .

Аналитические и вычислительные методы в теории вероятностей и её приложениях (АВМТВ-2017) = Analytical and Computational Methods in Probability Theory and its Applications (ACMPT-2017) : материалы Международной научной конференции. Россия, Москва, 23–27 октября 2017 г. . М. : Российский университет дружбы народов, 2017. p. 161-165.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review

Harvard

Rusakov, OV 2017, From the Pseudo-Poisson Processes with the Random Intensity to the Fractional Brownian Motion. in Аналитические и вычислительные методы в теории вероятностей и её приложениях (АВМТВ-2017) = Analytical and Computational Methods in Probability Theory and its Applications (ACMPT-2017) : материалы Международной научной конференции. Россия, Москва, 23–27 октября 2017 г. . Российский университет дружбы народов, М., pp. 161-165, 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, Russian Federation, 23/10/17.

APA

Rusakov, O. V. (2017). From the Pseudo-Poisson Processes with the Random Intensity to the Fractional Brownian Motion. In Аналитические и вычислительные методы в теории вероятностей и её приложениях (АВМТВ-2017) = Analytical and Computational Methods in Probability Theory and its Applications (ACMPT-2017) : материалы Международной научной конференции. Россия, Москва, 23–27 октября 2017 г. (pp. 161-165). Российский университет дружбы народов.

Vancouver

Rusakov OV. From the Pseudo-Poisson Processes with the Random Intensity to the Fractional Brownian Motion. In Аналитические и вычислительные методы в теории вероятностей и её приложениях (АВМТВ-2017) = Analytical and Computational Methods in Probability Theory and its Applications (ACMPT-2017) : материалы Международной научной конференции. Россия, Москва, 23–27 октября 2017 г. . М.: Российский университет дружбы народов. 2017. p. 161-165

Author

Rusakov, O. V. . / From the Pseudo-Poisson Processes with the Random Intensity to the Fractional Brownian Motion. Аналитические и вычислительные методы в теории вероятностей и её приложениях (АВМТВ-2017) = Analytical and Computational Methods in Probability Theory and its Applications (ACMPT-2017) : материалы Международной научной конференции. Россия, Москва, 23–27 октября 2017 г. . М. : Российский университет дружбы народов, 2017. pp. 161-165

BibTeX

@inproceedings{b759e0bcdeec468eb6dccd8e9b1cb14e,

title = "From the Pseudo-Poisson Processes with the Random Intensity to the Fractional Brownian Motion",

abstract = "We consider a Pseudo-Poisson process, when the leading Poissonprocess 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.",

keywords = "Pseudo-Poisson process, Laplace transform, Lamperti transform, fractional Ornstein-Uhlenbeck process, fractional Brownian Motion, Pseudo-Poisson process, Laplace transform, Lamperti transform, fractional Ornstein-Uhlenbeck process, fractional Brownian Motion",

author = "Rusakov, {O. V.}",

year = "2017",

language = "English",

isbn = "9785209082910",

pages = "161--165",

booktitle = "Аналитические и вычислительные методы в теории вероятностей и её приложениях (АВМТВ-2017) = Analytical and Computational Methods in Probability Theory and its Applications (ACMPT-2017)",

publisher = "Российский университет дружбы народов",

address = "Russian Federation",

note = "null ; Conference date: 23-10-2017 Through 27-10-2017",

}

RIS

TY - GEN

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

AU - Rusakov, O. V.

PY - 2017

Y1 - 2017

N2 - We consider a Pseudo-Poisson process, when the leading Poissonprocess 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.

AB - We consider a Pseudo-Poisson process, when the leading Poissonprocess 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.

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

UR - https://pure.spbu.ru/admin/files/15544544/ACMPT_2017_conference_proceedings.pdf

M3 - Conference contribution

SN - 9785209082910

SP - 161

EP - 165

BT - Аналитические и вычислительные методы в теории вероятностей и её приложениях (АВМТВ-2017) = Analytical and Computational Methods in Probability Theory and its Applications (ACMPT-2017)

PB - Российский университет дружбы народов

CY - М.

Y2 - 23 October 2017 through 27 October 2017

ER -

ID: 97764421