Expansion of transition distributions of Lévy processes in small time (Q1611564)

Let \(X\) be a real Lévy process. This paper gives a series expansion as \(t\) tends to 0 of its transition distribution function (in full generality on \(X\)) and of its transition density (when both density and jumping measure of \(X\) are smooth). It also proves the vague convergence of the normalized semigroup against the Lévy measure when \(t\) tends to 0, for a class of functions increasing moderately at infinity.