On the Gaussian Volterra processes with power-type kernels

We consider the Gaussian Volterra process Xθ={Xθ(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 Xθ 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.