English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Let the Ornstein–Uhlenbeck process $$(X_t)_{t\ge 0}$$ ( X t ) t ≥ 0 driven by a fractional Brownian motion $$B^{H }$$ B H described by $$dX_t = -\theta X_t dt + \sigma dB_t^{H }$$ d X t = - θ X t d t + σ d B t H be observed at discrete time instants $$t_k=kh$$ t k = k h , $$k=0, 1, 2, \ldots , 2n+2 $$ k = 0 , 1 , 2 , … , 2 n + 2 . We propose an ergodic type statistical estimator $${\hat{\theta }}_n $$ θ ^ n , $${\hat{H}}_n $$ H ^ n and $${\hat{\sigma }}_n $$ σ ^ n to estimate all the parameters $$\theta $$ θ , H and $$\sigma $$ σ in the above Ornstein–Uhlenbeck model simultaneously. We prove the strong consistence and the rate of convergence of the estimator. The step size h can be arbitrarily fixed and will not be forced to go zero, which is usually a reality. The tools to use are the generalized moment approach (via ergodic theorem) and the Malliavin calculus.

Estimation of all parameters in the fractional Ornstein–Uhlenbeck model under discrete observations