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Transfer Principle for nth order Fractional Brownian Motion with Applications to Prediction and Equivalence in Law
(2018)
- article
The n-th order fractional Brownian motion was introduced by Perrin et al. [13]. It is the (up to a multiplicative constant) unique self-similar Gaussian process with the Hurst index H∈(n-1,n), having n-th order stationary ...
Asymptotic normality of randomized periodogram for estimating quadratic variation in mixed Brownian–fractional Brownian model
(VTeX, 2015-05-11)
- article
We study asymptotic normality of the randomized periodogram estimator of quadratic variation in the mixed Brownian–fractional Brownian model. In the semimartingale case, that is, where the Hurst parameter H of the fractional ...
Prediction law of fractional Brownian motion
(Elsevier, 2017-10-01)
- article
We calculate the regular conditional future law of the fractional Brownian motion with index H ∈(0, 1) conditioned on its past. We show that the conditional law is continuous with respect to the conditioning path. We ...