Weak convergence and large deviations for RVβ Volterra–Lévy processes

We study Volterra–Lévy processeswith kernels regularly varying at infinity. We prove the weak convergence of rescaled processes to Gaussian limits with explicit covariance structures and establish large and moderate deviation principles. The analysis combines regular variation techniques, cumulant methods, and the Gärtner–Ellis theorem, extending classical asymptotic results for Lévy processes to the Volterra framework. The results are obtained for finite-dimensional distributions.