scholarly journals Drift parameter estimation for infinite-dimensional fractional Ornstein–Uhlenbeck process

2013 ◽  
Vol 137 (7) ◽  
pp. 880-901 ◽  
Author(s):  
Bohdan Maslowski ◽  
Ciprian A. Tudor
Keyword(s):  
Parameter Estimation ◽  
Uhlenbeck Process ◽  
Infinite Dimensional ◽  
Ornstein Uhlenbeck Process ◽  
Drift Parameter

scholarly journals Berry–Esséen bound for the parameter estimation of fractional Ornstein–Uhlenbeck processes

2019 ◽  
Vol 20 (04) ◽  
pp. 2050023 ◽  
Author(s):  
Yong Chen ◽  
Nenghui Kuang ◽  
Ying Li
Keyword(s):  
Parameter Estimation ◽  
Brownian Motion ◽  
Continuous Time ◽  
Index Formula ◽  
Hurst Index ◽  
Uhlenbeck Process ◽  
Ornstein Uhlenbeck Process ◽  
Time Observation ◽  
Statistical Estimations ◽  
Drift Parameter

For an Ornstein–Uhlenbeck process driven by fractional Brownian motion with Hurst index [Formula: see text], we show the Berry–Esséen bound of the least squares estimator of the drift parameter based on the continuous-time observation. We use an approach based on Malliavin calculus given by Kim and Park [Optimal Berry–Esséen bound for statistical estimations and its application to SPDE, J. Multivariate Anal. 155 (2017) 284–304].

scholarly journals A Special Study of the Mixed Weighted Fractional Brownian Motion

2021 ◽  
Vol 5 (4) ◽  
pp. 192
Author(s):  
Anas D. Khalaf ◽  
Anwar Zeb ◽  
Tareq Saeed ◽  
Mahmoud Abouagwa ◽  
Salih Djilali ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Estimation Problem ◽  
Special Study ◽  
Parameter Estimation Problem ◽  
Uhlenbeck Process ◽  
Sample Paths ◽  
Ornstein Uhlenbeck Process ◽  
Drift Parameter

In this work, we present the analysis of a mixed weighted fractional Brownian motion, defined by ηt:=Bt+ξt, where B is a Brownian motion and ξ is an independent weighted fractional Brownian motion. We also consider the parameter estimation problem for the drift parameter θ>0 in the mixed weighted fractional Ornstein–Uhlenbeck model of the form X0=0;Xt=θXtdt+dηt. Moreover, a simulation is given of sample paths of the mixed weighted fractional Ornstein–Uhlenbeck process.

scholarly journals About the infinite dimensional skew and obliquely reflected Ornstein–Uhlenbeck process

2015 ◽  
Vol 18 (04) ◽  
pp. 1550031
Author(s):  
Michael Röckner ◽  
Gerald Trutnau
Keyword(s):  
Real Hilbert Space ◽  
Monotonicity Condition ◽  
Normal Vector ◽  
Reflection Point ◽  
Uhlenbeck Process ◽  
Infinite Dimensional ◽  
Ornstein Uhlenbeck Process ◽  
Integration By Parts Formula ◽  
Regular Convex ◽  
Convex Subsets

Based on an integration by parts formula for closed and convex subsets [Formula: see text] of a separable real Hilbert space [Formula: see text] with respect to a Gaussian measure, we first construct and identify the infinite dimensional analogue of the obliquely reflected Ornstein–Uhlenbeck process (perturbed by a bounded drift [Formula: see text]) by means of a Skorokhod type decomposition. The variable oblique reflection at a reflection point of the boundary [Formula: see text] is uniquely described through a reflection angle and a direction in the tangent space (more precisely through an element of the orthogonal complement of the normal vector) at the reflection point. In case of normal reflection at the boundary of a regular convex set and under some monotonicity condition on [Formula: see text], we prove the existence and uniqueness of a strong solution to the corresponding SDE. Subsequently, we consider an increasing sequence [Formula: see text] of closed and convex subsets of [Formula: see text] and the skew reflection problem at the boundaries of this sequence. We present concrete examples and obtain as a special case the infinite dimensional analogue of the [Formula: see text]-skew reflected Ornstein–Uhlenbeck process.

Speed of Convergence of the Maximum Likelihood Estimator in the Ornstein-Uhlenbeck Process

1995 ◽  
Vol 45 (3-4) ◽  
pp. 245-252 ◽  
Author(s):  
J. P. N. Bishwal ◽  
Arup Bose
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Subject Classification ◽  
Speed Of Convergence ◽  
Primary 62F12 ◽  
Likelihood Estimator ◽  
Uhlenbeck Process ◽  
Ornstein Uhlenbeck Process ◽  
Drift Parameter

Berry-Bsseen bounds with random norming and Jario deviation probabilities arc derived for the maximum likelihood estimator of the drift parameter in tho Ornstoin-Uhlenbeck proccss. AMS (1991) Subject Classification: Primary 62F12, 62M05 Secondary 60FOS, 60F10

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