Adaptive Pointwise Estimation for Pure Jump Lévy Processes

Abstract

This paper is concerned with adaptive kernel estimation of the Lévy density N(x) for bounded-variation pure-jump Lévy processes. The sample path is observed at n discrete instants in the ”high frequency” context (∆ = ∆(n) tends to zero while n∆ tends to infinity). We construct a collection of kernel estimators of the function g(x) = xN(x) and propose a… (More)

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