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  • 1
    Electronic Resource
    Electronic Resource
    Estimating the Diffusion Coefficient for Diffusions Driven by fBm (2000)
    Springer
    Statistical inference for stochastic processes 3 (2000), S. 183-192 
    Details
    ISSN: 1572-9311
    Keywords: fractional Brownian motion ; local times ; nonparametric estimation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract When the Hurst coefficient of a fBm B t H is greater than 1/2, it is possible to define a stochastic integral with respect to B t H as the pathwise limit of Riemann sums. In this article we consider diffusion equations of the type Xt = x0 + ∫0 T σ (Xs) dBs H. We then construct a simple-to-use estimator of the diffusion coefficient σ(x), based on the number of crossings of level x of the process X t. We then study consistency in probability of this estimator and calculate convergence rates in probability.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1009981317912
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Central Limit Theorems for the Number of Maxima and an Estimator of the Second Spectral Moment of a Stationary Gaussian Process, with Application to Hydroscience (2000)
    Springer
    Extremes 3 (2000), S. 57-86 
    Details
    ISSN: 1572-915X
    Keywords: asymptotic variance ; central limit theorem ; crossings ; estimation ; Gaussian processes ; Hermite polynomials ; hydroscience ; maxima ; spectral moment
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let X = (Xt, t ≥ 0) be a mean zero stationary Gaussian process with variance one, assumed to satisfy some conditions on its covariance function r. Central limit theorems and asymptotic variance formulas are provided for estimators of the square root of the second spectral moment of the process and for the number of maxima in an interval, with some applications in hydroscience. A consistent estimator of the asymptotic variance is proposed for the number of maxima.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1009975204538
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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