Problem of simulation of multivariate Lévy processes is investigated. The method based on shot noise series expansions of such processes combined with Gaussian approximation of the remainder is established in full generality. Formulas that can be used for simulation of tempered stable, operator stable and other multivariate processes are obtained. Key-words: Lévy processes, Gaussian approximati...

Multivariate Lévy-driven mixed moving average (MMA) processes of the type Xt = ∫ ∫ f(A, t − s)Λ(dA, ds) cover a wide range of well known and extensively used processes such as Ornstein-Uhlenbeck processes, superpositions of Ornstein-Uhlenbeck (supOU) processes, (fractionally integrated) CARMA processes and increments of fractional Lévy processes. In this paper, we introduce multivariate MMA pro...

A multivariate generalisation of the Whittle likelihood is used to extend spectral subsampling MCMC stationary time series by matrix-valued periodogram observations in frequency domain. To assess performance methodology challenging problems, a autoregressive tempered fractionally integrated moving average model (ARTFIMA) introduced and some its properties derived. Bayesian inference based on de...

In this paper, we show that in order to obtain the Tsallis entropy rate for stochastic processes, we can use the limit of conditional entropy, as it was done for the case of Shannon and Renyi entropy rates. Using that we can obtain Tsallis entropy rate for stationary Gaussian processes. Finally, we derive the relation between Renyi, Shannon and Tsallis entropy rates for stationary Gaussian proc...

The problem of simulation of multivariate Lévy processes is investigated. A method based on generalized shot noise series representations of Lévy processes combined with Gaussian approximation of the remainder is established in full generality. This method is applied to multivariate stable and tempered stable processes and formulas for their approximate simulation are obtained. Key-words: Lévy ...