On Centering 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.

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...

Isotropic Infinitely Divisible Processes on Compact Symmetric Spaces

Let G be a connected compact Lie group, K a compact subgroup, such that G/K is a Riemannian symmetric homogeneous space. (See [l ] for terminology and notation.) We fix once and for all a G-invariant metric on G/K. D(G/K) will stand for the algebra of those differential operators on C°°(G/.K) which are invariant under the action of G. S(K\G/K) stands for the semi-group, under convolution as pro...

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