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1
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Computer-aided modeling and simulation of electrical circuits with α-stable noise

100%
Weron A.
Applicationes Mathematicae
|
1995-1996
|
tom 23
|
nr 1
83-93
EN
The aim of this paper is to demonstrate how the appropriate numerical, statistical and computer techniques can be successfully applied to the construction of approximate solutions of stochastic differential equations modeling some engineering systems subject to large disturbances. In particular, the evolution in time of densities of stochastic processes solving such problems is discussed.
2
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A remark on disjointness results for stable processes

100%
Weron A.
Studia Mathematica
|
1993
|
tom 105
|
nr 3
253-254
3
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Approximation of stochastic differential equations driven by α-stable Lévy motion

51%
Janicki A., Michna Z., Weron A.
Applicationes Mathematicae
|
1996-1997
|
tom 24
|
nr 2
149-168
EN
In this paper we present a result on convergence of approximate solutions of stochastic differential equations involving integrals with respect to α-stable Lévy motion. We prove an appropriate weak limit theorem, which does not follow from known results on stability properties of stochastic differential equations driven by semimartingales. It assures convergence in law in the Skorokhod topology of sequences of approximate solutions and justifies discrete time schemes applied in computer simulations. An example is included in order to demonstrate that stochastic differential equations with jumps are of interest in constructions of models for various problems arising in science and engineering, often providing better description of real life phenomena than their Gaussian counterparts. In order to demonstrate the usefulness of our approach, we present computer simulations of a continuous time α-stable model of cumulative gain in the Duffie-Harrison option pricing framework.
4
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What is the best approximation of ruin probability in infinite time?

51%
Burnecki K., Miśta P., Weron A.
Applicationes Mathematicae
|
2005
|
tom 32
|
nr 2
155-176
EN
We compare 12 different approximations of ruin probability in infinite time studying typical light- and heavy-tailed claim size distributions, namely exponential, mixture of exponentials, gamma, lognormal, Weibull, loggamma, Pareto and Burr. We show that approximation based on the Pollaczek-Khinchin formula gives most accurate results, in fact it can be chosen as a reference method. We also introduce a promising modification to the De Vylder approximation.
5
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Asymptotic behaviour of stochastic systems with conditionally exponential decay property

51%
Jurlewicz A., Weron A., Weron K.
Applicationes Mathematicae
|
1995-1996
|
tom 23
|
nr 4
379-394
EN
A new class of CED systems, providing insight into behaviour of physical disordered materials, is introduced. It includes systems in which the conditionally exponential decay property can be attached to each entity. A limit theorem for the normalized minimum of a CED system is proved. Employing different stable schemes the universal characteristics of the behaviour of such systems are derived.
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