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1
Content available remote On Lamperti stable processes
Caballero M. E., Pardo J. C., Pérez J. L.
Probability and Mathematical Statistics
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2010
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Vol. 30, Fasc. 1
1--28
EN
In this paper, we consider a new family of Rd-valued Lévy processes that we call Lamperti stable. One of the advantages of this class is that the law of many related functionals can be computed explicitly. In the one-dimensional case we provide an explicit form for the characteristic exponent and other several useful properties of the class. This family of processes shares many tractable properties with the tempered stable and the layered stable processes, defined by Rosiński [33] and Houdré and Kawai [16], respectively. We also find a series representation which is used for sample path simulation, illustrated in the case d = 1. Finally, we provide many examples, some of which appear in recent literature.
2
Content available remote Limiting behaviour of Dirichlet forms for stable processes on metric spaces
Pietruska-Pałuba K.
Bulletin of the Polish Academy of Sciences. Mathematics
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2008
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Vol. 56, no 3-4
257-266
EN
Supposing that the metric space in question supports a fractional diffusion, we prove that after introducing an appropriate multiplicative factor, the Gagliardo seminorms ||ƒ||wσ,2 of a function ƒ ∈ L²(E, μ) have the property [wzór...] where ε is the Dirichlet form relative to the fractional diffusion.
3
Content available remote Metric entropy and the small deviation problem for stable processes
Aurzada F.
Probability and Mathematical Statistics
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2007
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Vol. 27, Fasc. 2
261--274
EN
The famous connection between metric entropy and small deviation probabilities of Gaussian processes was discovered by Kuelbs and Li in [6] and completed by Li and Linde in [9]. The question whether similar connections exist for other types of processes has remained open ever since. In [10], Li and Linde propose a first approach to this problem for stable processes. The present article clarifies the question completely for symmetric stable processes.
4
Content available remote Minimal integral representations of stable processes
Rosiński J.
Probability and Mathematical Statistics
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2006
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Vol. 26, Fasc. 1
121--142
EN
Minimal integral representations are defined for general stochastic processes and completely characterized for stable processes (symmetric and asymmetric). In the stable case, minimal representations are described by rigid subsets of the Lp-spaces which are investigated here in detail. Exploiting this relationship, various tests for the minimality of representations of stable processes are obtained and used to verify this property for many representations of processes of interest.
5
Content available remote Fractional derivatives of local times of stable Lévy processes as the limits of the occupation time problem in Besov space
Ouhara M. A., Eddahbi M., Ouali M.
Probability and Mathematical Statistics
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2004
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Vol. 24, Fasc. 2
263--279
EN
In this paper, we firstly study the Besov regularity of the local time of symmetric stable processes and of its fractional derivative. Secondly, we establish limit theorems for occupation times of α-symmetric stable processes with 1 < α ≤ 2 in some Besov spaces. Finally, we give the strong approximation version of our limit theorems.
6
Content available remote Potential theory for Lévy stable processes
Bogdan K., Stós A., Sztonyk P.
Bulletin of the Polish Academy of Sciences. Mathematics
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2002
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Vol. 50, no 3
361-372
EN
We investigate properties of functions that are harmonic with respect to symmetric stable processes which are not necessarily rotation invariant. We prove the Harnack inequality and the boundary Harnack principle for a Lipschitz domain. To obtain this we use Poisson kernel estimates. We also give an estimate concerning the rate of decay of harmonic functions near the boundary of the domain.
7
Content available remote Symmetric [alpha]-stable processesof d-sets
Stos A.
Bulletin of the Polish Academy of Sciences. Mathematics
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2000
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Vol. 48, no 3
237-245
EN
The aim of the paper is to investigate symmetric [alpha]-stable processes on d-sets and identify corresponding Dirichlet forms.
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