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/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

We consider a recurrent Markov process which is an It\^o semi-martingale. TheL\'evy kernel describes the law of its jumps. Based on observationsX(0),X({\Delta}),...,X(n{\Delta}), we construct an estimator for the L\'evykernel's density. We prove its consistency (as n{\Delta}->\infty and{\Delta}->0) and a central limit theorem. In the positive recurrent case, ourestimator is asymptotically normal; in the null recurrent case, it isasymptotically mixed normal. Our estimator's rate of convergence equals thenon-parametric minimax rate of smooth density estimation. The asymptotic biasand variance are analogous to those of the classical Nadaraya-Watson estimatorfor conditional densities. Asymptotic confidence intervals are provided.

On Non-parametric Estimation of the L\'evy Kernel of Markov Processes