On the Gaussian Volterra processes with power-type kernels

Abstract

We consider the Gaussian Volterra process X θ = { X θ ( t ) , t ∈ [ 0 , T ] } , θ = ( α , β , γ ) introduced in Mishura and Shklyar [Theory and Applications 2022a, 431–452] We specify the parameters θ for which X θ is non Markovian, semimartingale, and exhibits long-range dependence. Finally, by using its Paley–Wiener–Zygmund representation we establish its continuity in θ, uniformly in t.