Asymptotic equivalence of jumps Lévy processes and their discrete counterpart

Abstract

We establish the global asymptotic equivalence between a pure jumps Lévy process $\{X_t\}$ on the time interval $[0,T]$ with unknown Lévy measure $\nu$ belonging to a non-parametric class and the observation of $2m^2$ Poisson independent random variables with parameters linked with the Lévy measure $\nu$. The equivalence result is asymptotic as $m$ tends to infinity. The time $T$ is kept fixed and the sample path is continuously observed. This result justifies the idea that, from a statistical point of view, knowing how many jumps fall into a grid of intervals gives asymptotically the same amount of information as observing $\{X_t\}$.

Shorter version focusing on the statistical analysis of the Lévy measure. A new example has been added

References in corpus (4)

• Asymptotic Equivalence for Nonparametric Regression
• Asymptotic equivalence of functional linear regression and a white noise inverse problem
• Nonparametric inference for discretely sampled Lévy processes
• Limit experiments of GARCH

Cited by in corpus (1)

• Asymptotic equivalence for inhomogeneous jump diffusion processes and white noise