Statistical Analysis of the Fractional Ornstein–Uhlenbeck Type Process

By Marina L. Kleptsyna, Alain Le Breton. 2002

294 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/1286d9b65a0fd17a70dc0ca5ea79473486cc773c

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Citations in the corpus

Asymptotic properties of MLE for partially observed fractional diffusion system (2010, methodology): “From [12], the explicit expression of the Laplace transform LT (a, θ) is given by:”
On drift parameter estimation in models with fractional Brownian motion (2011, methodology): “Our idea was to generalize their result for the coefficients that are not constant, so that the method from [3] does not work however for the case when the coefficients are sufficiently close to constants so that the result σ 2 T T → ∞ still holds.”
Optimal rates for parameter estimation of stationary Gaussian processes (2016, methodology): “arameters in fBm-driven models, which have been developed over the course of the past 10 or 15 years. The approaches we mention below are related to the methods in this article. • The MLE approach in [17], [27]. In general the techniques used to construct maximum likelihood estimators (MLE) for drif”
Parameter estimation for a partially observed Ornstein–Uhlenbeck process with long-memory noise (2015, background): “1 Context and background The question of drift parameter estimation for solutions of stochastic differential equations driven by fractional Brownian noise goes back at least as far as the seminar work of Kleptsyna and Le Breton in [17] (also see prior references therein), where a maximum likelihood ”
Least squares estimator for non-ergodic Ornstein-Uhlenbeck processes driven by Gaussian processes (2015, methodology): “We will recall several approaches to estimate the parameters in fractional models but we mention that the list below is not exhaustive: - The MLE approach in [12], [16]: In general the techniques used to construct maximum likelihood estimators (MLE) for the drift parameter are based on Girsanov’s tr”
Sharp Large Deviations for the Fractional Ornstein–Uhlenbeck Process (2008, methodology): “The almost sure convergence of θ̂T towards θ was already proven by Kleptsyna and Le Breton [10], see also Prakasa Rao [13, 14] for related results.”
Parameter estimation for fractional Ornstein–Uhlenbeck processes (2009, background): “In [8], the the maximum likelihood estimator θ̄T for the parameter θ is obtained and has the following expression”
Statistical aspects of the fractional stochastic calculus (2006, methodology): “where Q t = d d!H Z t 0 k(t; s)Xsds; t 2 [0; T ]: (39) By using Girsanov's theorem (see [29] and [23]) we obtain that the MLE is given by”