Simple conditions for mixing of infinitely divisible processes

Log-infinitely divisible multifractal processes

We define a large class of multifractal random measures and processes with arbitrary loginfinitely divisible exact or asymptotic scaling law. These processes generalize within a unified framework both the recently defined log-normal Multifractal Random Walk processes (MRW) [33, 3] and the log-Poisson “product of cynlindrical pulses” [7]. Their construction involves some “continuous stochastic m...

Ergodic Properties of Max–Infinitely Divisible Processes

We prove that a stationary max–infinitely divisible process is mixing (ergodic) iff its dependence function converges to 0 (is Cesaro summable to 0). These criteria are applied to some classes of max–infinitely divisible processes.

Mixing Conditions for Multivariate Infinitely Divisible Processes with an Application to Mixed Moving Averages and the supOU Stochastic Volatility Model

We consider strictly stationary infinitely divisible processes and first extend the mixing conditions given in Maruyama [18] and Rosiński and Żak [23] from the univariate to the d-dimensional case. Thereafter, we show that multivariate Lévy-driven mixed moving average processes satisfy these conditions and hence a wide range of well-known processes such as superpositions of Ornstein-Uhlenbeck (...

Tempered infinitely divisible distributions and processes

In this paper, we construct the new class of tempered infinitely divisible (TID) distributions. Taking into account the tempered stable distribution class, as introduced by in the seminal work of Rosińsky [10], a modification of the tempering function allows one to obtain suitable properties. In particular, TID distributions may have exponential moments of any order and conserve all proper prop...

Symmetric infinitely divisible processes with sample paths in Orlicz spaces and absolute continuity of infinitely divisible processes