Displaying similar documents to “Consistent non-parametric bayesian estimation for a time-inhomogeneous brownian motion”

Local estimation of the Hurst index of multifractional brownian motion by increment ratio statistic method

Pierre Raphaël Bertrand, Mehdi Fhima, Arnaud Guillin (2013)

ESAIM: Probability and Statistics

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We investigate here the central limit theorem of the increment ratio statistic of a multifractional Brownian motion, leading to a CLT for the time varying Hurst index. The proofs are quite simple relying on Breuer–Major theorems and an original strategy. A simulation study shows the goodness of fit of this estimator.

Revisiting the sample path of Brownian motion

S. James Taylor (2006)

Banach Center Publications

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Brownian motion is the most studied of all stochastic processes; it is also the basis for stochastic analysis developed in the second half of the 20th century. The fine properties of the sample path of a Brownian motion have been carefully studied, starting with the fundamental work of Paul Lévy who also considered more general processes with independent increments and extended the Brownian motion results to this class. Lévy showed that a Brownian path in d (d ≥ 2) dimensions had zero...