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Stochastic representation and path properties of a fractional Cox–Ingersoll–Ross processстатья
Информация о цитировании статьи получена из
Web of Science,
Scopus
Дата последнего поиска статьи во внешних источниках: 2 сентября 2020 г.
- Авторы: Mishura Yu S., Piterbarg V.I., Ralchenko K.V., Yurchenko-Tytarenko Yu A.
- Журнал: Theory of Probability and Mathematical Statistics
- Том: 97
- Год издания: 2018
- Первая страница: 167
- Последняя страница: 182
- DOI: 10.1090/tpms/1055
- Аннотация: We consider the Cox–Ingersoll–Ross process that satisfies the stochastic differential equation dX_t = aX_tdt + σ√X_tdBH_t driven by a fractional Brownian motion BH_t with the Hurst index exceeding 2/3. We show that the Cox–Ingersoll–Ross process coincides with the square of the fractional Ornstein– Uhlenbeck process up to the first return to zero. Based on this observation, we consider the square of the fractional Ornstein–Uhlenbeck process with an arbitrary Hurst index and prove that it satisfies the above stochastic differential equation up to the first return to zero if t0√XsdBHs is understood as the pathwise Stratonovich integral. Then a natural question arises about the first visit to zero of the fractional Cox–Ingersoll–Ross process which coincides with the first visit to zero of the fractional Ornstein–Uhlenbeck process. Since the latter process is Gaussian, we use the bounds for the distributions of Gaussian processes to prove that the probability of a visit to zero over a finite time equals 1 if a < 0. Otherwise this probability is positive. We provide an upper bound for this probability.
- Добавил в систему: Питербарг Владимир Ильич