
Maximum likelihood estimation for subfractional Vasicek model
We investigate the asymptotic properties of maximum likelihood estimator...
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Hurst index estimation in stochastic differential equations driven by fractional Brownian motion
We consider the problem of Hurst index estimation for solutions of stoch...
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Drift Estimation for Discretely Sampled SPDEs
The aim of this paper is to study the asymptotic properties of the maxim...
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Statistical inference for Vasicektype model driven by Hermite processes
Let (Z^q, H_t)_t ≥ 0 denote a Hermite process of order q ≥ 1 and selfsi...
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Entropy flow and De Bruijn's identity for a class of stochastic differential equations driven by fractional Brownian motion
Motivated by the classical De Bruijn's identity for the additive Gaussia...
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Asymptotic preserving schemes for SDEs driven by fractional Brownian motion in the averaging regime
We design numerical schemes for a class of slowfast systems of stochast...
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A generalized Avikainen's estimate and its applications
Avikainen provided a sharp upper bound of the difference E[g(X)g(X)^q...
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Increasing Domain Infill Asymptotics for Stochastic Differential Equations Driven by Fractional Brownian Motion
Although statistical inference in stochastic differential equations (SDEs) driven by Wiener process has received significant attention in the literature, inference in those driven by fractional Brownian motion seem to have seen much less development in comparison, despite their importance in modeling long range dependence. In this article, we consider both classical and Bayesian inference in such fractional Brownian motion based SDEs. In particular, we consider asymptotic inference for two parameters in this regard; a multiplicative parameter associated with the drift function, and the socalled "Hurst parameter" of the fractional Brownian motion, when the time domain tends to infinity. For unknown Hurst parameter, the likelihood does not lend itself amenable to the popular Girsanov form, rendering usual asymptotic development difficult. As such, we develop increasing domain infill asymptotic theory, by discretizing the SDE. In this setup, we establish consistency and asymptotic normality of the maximum likelihood estimators, as well as consistency and asymptotic normality of the Bayesian posterior distributions. However, classical or Bayesian asymptotic normality with respect to the Hurst parameter could not be established. We supplement our theoretical investigations with simulation studies in a nonasymptotic setup, prescribing suitable methodologies for classical and Bayesian analyses of SDEs driven by fractional Brownian motion.
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