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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We study nonparametric estimation of the diffusion coefficient from discretedata, when the observations are blurred by additional noise. Such issues havebeen developed over the last 10 years in several application fields and inparticular in high frequency financial data modelling, however mainly from aparametric and semiparametric point of view. This paper addresses thenonparametric estimation of the path of the (possibly stochastic) diffusioncoefficient in a relatively general setting. By developing pre-averagingtechniques combined with wavelet thresholding, we construct adaptive estimatorsthat achieve a nearly optimal rate within a large scale of smoothnessconstraints of Besov type. Since the diffusion coefficient is usually genuinelyrandom, we propose a new criterion to assess the quality of estimation; weretrieve the usual minimax theory when this approach is restricted to adeterministic diffusion coefficient. In particular, we take advantage of recentresults of Reiss [33] of asymptotic equivalence between a Gaussian diffusionwith additive noise and Gaussian white noise model, in order to prove a sharplower bound.

Adaptive wavelet estimation of the diffusion coefficient under additive error measurements