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Piterbarg, Yuliya Mishura","submitted_at":"2017-08-09T04:30:53Z","abstract_excerpt":"We consider the fractional Cox-Ingersoll-Ross process satisfying the stochastic differential equation (SDE) $dX_t = aX_t\\,dt + \\sigma \\sqrt{X_t}\\,dB^H_t$ driven by a fractional Brownian motion (fBm) with Hurst parameter exceeding $\\frac{2}{3}$. The integral $\\int_0^t\\sqrt{X_s}dB^H_s$ is considered as a pathwise integral and is equal to the limit of Riemann-Stieltjes integral sums. It is shown that the fractional Cox-Ingersoll-Ross process is a square of the fractional Ornstein-Uhlenbeck process until the first zero hitting. 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