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- Jan Rosiński
- 2007

Several methods of generating series representations of a Lévy process are presented under a unified approach and a new rejection method is introduced in this context. The connection of such representations with the Lévy–Itô integral representation is precisely established. Four series representations of a gamma process are given as illustrations of these… (More)

- Jan Rosiński
- 2004

A tempered stable Lévy process combines both the α–stable and Gaussian trends. In a short time frame it is close to an α–stable process while in a long time frame it approximates a Brownian motion. In this paper we consider a general and robust class of multivariate tempered stable distributions and establish their identifiable parametrization. We prove… (More)

- Serge Cohen, Jan Rosiński
- 2006

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… (More)

- BY MARTIN JACOBSEN, THOMAS MIKOSCH, JAN ROSIŃSKI
- 2009

In this paper, we consider certain σ-finite measures which can be interpreted as the output of a linear filter. We assume that these measures have regularly varying tails and study whether the input to the linear filter must have regularly varying tails as well. This turns out to be related to the presence of a particular cancellation property in σ-finite… (More)

- Jan Rosiński, Kazimierz Urbanik
- 2006

Minimal integral representations are defined for general stochastic processes and completely characterized for stable processes (symmetric and nonsymmetric). In the stable case, minimal representations are described by rigid subsets of the L p-spaces which are investigated here in detail. Exploiting this relationship, various tests for the minimality of… (More)

- IVAN NOURDIN, JAN ROSIŃSKI
- 2011

We characterize the asymptotic independence between blocks consisting of multiple Wiener-Itô integrals. As a consequence of this characterization, we derive the celebrated fourth moment theorem of Nualart and Peccati, its multidimensional extension, and other related results on the multivariate convergence of multiple Wiener-Itô integrals, that involve… (More)

- Jan Rosiński
- 2007

We show that for each weakly majorizing measure there is a natural metric with respect to which sample paths of stochastic processes are Hölder continuous and their Hölder norm satisfies a strong integrability condition. We call such metric a minorizing metric. The class of minorizing metrics is minimal among all metrics assuring sample Hölder continuity of… (More)

Sufficient conditions for boundedness and continuity are obtained for stochastically continuous infinitely divisible processes, without Gaussian component, {Y (t), t ∈ T }, where T is a compact metric space or pseudo-metric space. Such processes have a version given by Y (t) = X(t) + b(t), t ∈ T where b is a deterministic drift function and X(t) = S f (t,… (More)

- TAKAHIRO AOYAMA, MAKOTO MAEJIMA, JAN ROSIŃSKI
- 2006

A new class of type G selfdecomposable distributions is introduced and characterized in terms of Lévy integrals. In dimension one, this class is a strict subclass of selfdecomposable variance mixtures of normal distributions. The relation to several other known classes of infinitely divisible distributions is established.

Two results are obtained concerning the continuity and local bound-edness of stochastic processes of the form (f * Z)(t) = t 0 f (t − s) dZ(s) t ≥ 0 where f : [0, ∞) → R is a continuous function with f (0) = 0 and Z is a semimartingale. One states that the process f * Z is not always continuous. Specifically, for any symmetric Lévy process Z with paths of… (More)