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RESEARCH PRODUCT

PARAMETER ESTIMATION FOR FRACTIONAL ORNSTEIN-UHLENBECK PROCESSES: NON-ERGODIC CASE

Rachid Belfadli Khalifa Es-sebaiy Youssef Ouknine

subject

[MATH.MATH-PR] Mathematics [math]/Probability [math.PR]Probability (math.PR)62F12 60G18 60G1562F12 60G18 60G15.[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]Mathematics::ProbabilityFOS: MathematicsParameter estimationYoung integralYoung integral.Parameter estimation; Non-ergodic fractional Ornstein-Uhlenbeck process; Young integral.[ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR]Mathematics - ProbabilityNon-ergodic fractional Ornstein-Uhlenbeck process

description

We consider the parameter estimation problem for the non-ergodic fractional Ornstein-Uhlenbeck process defined as $dX_t=\theta X_tdt+dB_t,\ t\geq0$, with a parameter $\theta>0$, where $B$ is a fractional Brownian motion of Hurst index $H\in(1/2,1)$. We study the consistency and the asymptotic distributions of the least squares estimator $\hat{\theta}_t$ of $\theta$ based on the observation $\{X_s,\ s\in[0,t]\}$ as $t\rightarrow\infty$.

yearjournalcountryeditionlanguage
2011-02-25
https://hal.archives-ouvertes.fr/hal-00569387