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Layered stable (multivariate) distributions and processes are defined and studied. A layered stable process combines stable trends of two different indices, one of them possibly Gaussian. More precisely, in short time, it is close to a stable process while, in long time, it approximates another stable (possibly Gaussian) process.
Christian Houdré, Reiichiro Kawai
exaly +7 more sources
Operator-stable-like processes [PDF]
In the present paper, we introduce so-called operator-stable-like processes. Roughly speaking, they behave locally like operator-stable processes, but they need not to be homogenous in space. Having shown existence for this class of processes, we analyze maximal estimates, the existence of moments, the short- and long-time behavior of the sample paths ...
Scheffler, Peter +2 more
openaire +3 more sources
Normal modified stable processes [PDF]
The authors discuss extensions of the concept of normal inverse Gaussian processes [see, for example, \textit{O. E. Barndorff-Nielsen}, Scand. J. Stat. 24, No. 1, 1-13 (1997; Zbl 0934.62109)] to the concept of normal modified stable processes. The family of normal inverse Gaussian distributions and the normal inverse Gaussian processes have been found ...
Barndorff-Nielsen, Ole Eiler +1 more
openaire +5 more sources
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Rosiński, Jan +2 more
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Parameter Estimation for SPDEs Driven by Cylindrical Stable Processes
We consider infinite dimensional extension of affine models with heavy tails in finance. We study several estimators of the drift parameter in the stochastic partial differential equation driven by cylindrical stable processes.
Jaya P. N. Bishwal
doaj +1 more source
Potentials of Stable Processes [PDF]
For a stable process, we give an explicit formula for the potential measure of the process killed outside a bounded interval and the joint law of the overshoot, undershoot and undershoot from the maximum at exit from a bounded interval. We obtain the equivalent quantities for a stable process reflected in its infimum.
Kyprianou, A. E., Watson, A. R.
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Classes of Mixing Stable Processes [PDF]
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jan Rosiński +2 more
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Understanding the hydrochemical evolutionary mechanisms of surface water and groundwater in saline-alkali wetlands in arid and semi-arid regions is necessary for assessing how wetland water resource utilization and restoration processes may affect the ...
Geng Cui +3 more
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Windings of Planar Stable Processes [PDF]
Using a generalization of the skew-product representation of planar Brownian motion and the analogue of Spitzer's celebrated asymptotic Theorem for stable processes due to Bertoin and Werner, for which we provide a new easy proof, we obtain some limit Theorems for the exit time from a cone of stable processes of index $α\in(0,2)$.
Vakeroudis, Stavros, Doney, Ron
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Multivariate extremes and max-stable processes: discussion of the paper by Zhengjun Zhang
This discussion reviews the paper by Zhengjun Zhang in the context of broader research on multivariate extreme value theory and max-stable processes.
R. L. Smith
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