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Keywords
(12)
Asymptotic Behaviour
Asymptotic Bias
fractional brownian motion
Laplace Transform
Maximum Likelihood Estimate
Mean Square Error
ornsteinuhlenbeck process
Statistical Analysis
Stochastic Differential Equation
Strong Consistency
brownian motion
ornstein uhlenbeck
Related Publications
(8)
Statistical aspects of the fractional stochastic calculus
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Statistical Analysis of the Fractional Ornstein–Uhlenbeck Type Process
Statistical Analysis of the Fractional Ornstein–Uhlenbeck Type Process,10.1023/A:1021220818545,Statistical Inference for Stochastic Processes,M. L. Kl
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Statistical Analysis of the Fractional Ornstein–Uhlenbeck Type Process
(
Citations: 38
)
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M. L. Kleptsyna
,
A. Le Breton
We consider the fractional analogue of the Ornstein–Uhlenbeck process, that is, the solution of a onedimensional homogeneous linear
stochastic differential equation
driven by a
fractional Brownian motion
in place of the usual Brownian motion. The statistical problem of estimation of the drift and variance parameters is investigated on the basis of a semimartingale which generates the same filtration as the observed process. The
asymptotic behaviour
of the
maximum likelihood
estimator of the drift parameter is analyzed.
Strong consistency
is proved and explicit formulas for the
asymptotic bias
and
mean square error
are derived. Preparing for the analysis, a change of probability method is developed to compute the
Laplace transform
of a quadratic functional of some auxiliary process.
Journal:
Statistical Inference for Stochastic Processes
, vol. 5, no. 3, pp. 229248, 2002
DOI:
10.1023/A:1021220818545
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Citation Context
(20)
...There has been a recent interest to study similar problems for stochastic processes driven by a fractional Brownian motion (fBm) starting with the works of Le Breton (1998 )a nd
Kleptsyna and Le Breton (2002)
...
M. N. Mishra
,
et al.
Nonparametric estimation of trend for stochastic differential equation...
...Following the notation introduced in Kleptsyna and LeBreton [
1
] (cf...
M. N. Mishra
,
et al.
Nonparametric Estimation of Linear Multiplier for Fractional Diffusion...
...The following facts are known from Kleptsyna and Le Breton [
11
]:...
...Kleptsyna and Le Breton [
11
] showed that ˆ θT is strongly consistent estimator of θ. Using the Fourier method, we prove a BerryEsseen type theorem for the estimator ˜ θT which gives the asymptotic normality...
...P r o o f. (a) Kleptsyna and Le Breton [
11
] proved the following Cameron...
...Kleptsyna and Le Breton [
11
] obtained the following fractional Cameron...
...P r o o f. We use analytic continuation, the fractional Itˆ o formula along with change of measure technique as in Liptser and Shiryayev [15] and Kleptsyna and Le Breton [
11
]...
...Now solving for R γ (T ) as in Kleptsyna and Le Breton [
11
], we get...
Jaya P. N. Bishwal
.
Minimum contrast estimation in fractional OrnsteinUhlenbeck process: ...
...In [
8
], the the maximum likelihood estimator ¯ �T for the parameter � is obtained and has the following expression...
Yaozhong Huand
,
et al.
Parameter estimation for fractional Ornstein–Uhlenbeck processes
...Such questions have been recently treated in several papers (see [
5
] for the case H ∈ ( 1 ,1) and b linear or [13] for the general case or [10] for the twoparameter...
Karine Bertin
,
et al.
Maximumlikelihood estimators and random walks in long memory models
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SIMULATION AND ESTIMATION OF LONG MEMORY CONTINUOUS TIME MODELS
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Citations: 26
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Stochastic Calculus for Fractional Brownian Motion. I: Theory1
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Siam Journal on Control and Optimization  SIAM
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Statistics of Random Processes: I
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R. S. Liptser
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A. N. Shiryaev
Published in 2000.
An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motion
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Sequential estimation of parameters of difiusion processes
(
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Published in 1971.
Sort by:
Citations
(38)
Nonparametric estimation of trend for stochastic differential equations driven by fractional Brownian motion
(
Citations: 1
)
M. N. Mishra
,
B. L. S. Prakasa Rao
Journal:
Statistical Inference for Stochastic Processes
, vol. 14, no. 2, pp. 101109, 2011
Nonparametric Estimation of Linear Multiplier for Fractional Diffusion Processes
M. N. Mishra
,
B. L. S. Prakasa Rao
Journal:
Stochastic Analysis and Applications  STOCHASTIC ANAL APPL
, vol. 29, no. 4, pp. 706712, 2011
Facteurs nutritionnels et risque de cancer de la cavité buccale
P. LatinoMartel
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N. DruesnePecollo
,
A. Dumond
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Revue De Stomatologie Et De Chirurgie Maxillofaciale  REV STOMATOL CHIR MAXILLOFAC
, vol. 112, no. 3, pp. 155159, 2011
Novel supramolecular gelation route to in situ entrapment and sustained delivery of plasmid DNA
Dong Ma
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HongBin Zhang
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DiHu Chen
,
LiMing Zhang
Journal:
Journal of Colloid and Interface Science  J COLLOID INTERFACE SCI
, vol. 364, no. 2, pp. 566573, 2011
Optimal sequential changedetection for fractional stochastic differential equations
Alexandra Chronopoulou
,
Georgios Fellouris
Published in 2011.