Local Holder Conditions for the Local Times of Certain Stationary Gaussian Processes

Local times and Sample Function Properties of Stationary Gaussian Processes

Gaussian processes and the local times of symmetric Lévy processes

We give a relatively simple proof of the necessary and sufficient condition for the joint continuity of the local times of symmetric Lévy processes. This result was obtained in 1988 by M. Barlow and J. Hawkes without requiring that the Lévy processes be symmetric. In 1992 the authors used a very different approach to obtain necessary and sufficient condition for the joint continuity of the loca...

L moduli of continuity of Gaussian processes and local times of symmetric Lévy processes

Let X = {X(t), t ∈ R+} be a real valued symmetric Lévy process with continuous local times {Lt , (t, x) ∈ R+ × R} and characteristic function EeiλX(t) = e−tψ(λ). Let σ 0(x− y) = 4 π ∞ ∫ 0 sin λ(x−y) 2 ψ(λ) dλ. If σ2 0(h) is concave, and satisfies some addtional very weak regularity conditions, then for any p ≥ 1, and all t ∈ R+

Lp moduli of continuity of Gaussian processes and local times of symmetric Levy processes

Let X = {X(t), t ∈ R+} be a real-valued symmetric Lévy process with continuous local times {L x t , (t, x) ∈ R+ × R} and characteristic function Ee iλX(t) = e −tψ(λ). Let σ 2 0 (x − y) = 4 π ∞ 0 sin 2 (λ(x − y)/2) ψ(λ) dλ. If σ 2 0 (h) is concave, and satisfies some additional very weak regularity conditions, then for any p ≥ 1, and all t ∈ R+, lim h↓0 b a L x+h t − L x t σ0(h) p dx = 2 p/2 E|η...

Moduli of Continuity of Local Times of Strongly Symmetric Markov Processes via Gaussian Processes

1. Introduction. In this paper we show that the moduli of continuity of the local times