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Simulation of infinitely divisible random fields
TLDR
Two methods to approximate infinitely divisible random fields are presented, based on approximating the kernel function in the spectral representation of such fields, leading to numerical integration of the respective integrals.Abstract:
Two methods to approximate infinitely divisible random fields are presented. The methods are based on approximating the kernel function in the spectral representation of such fields, leading to numerical integration of the respective integrals. Error bounds for the approximation error are derived and the approximations are used to simulate certain classes of infinitely divisible random fields.read more
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Journal ArticleDOI
Stable non-Gaussian random processes , by G. Samorodnitsky and M. S. Taqqu. Pp. 632. £49.50. 1994. ISBN 0-412-05171-0 (Chapman and Hall).
Book
Lévy processes and infinitely divisible distributions
TL;DR: In this paper, the authors consider the distributional properties of Levy processes and propose a potential theory for Levy processes, which is based on the Wiener-Hopf factorization.
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Spatial Process Generation
Dirk P. Kroese,Zdravko I. Botev +1 more
TL;DR: This paper describes how to generate realizations from the main types of spatial processes, including Gaussian and Markov random fields, point processes, spatial Wiener processes, and Levy fields.
Book ChapterDOI
Asymptotic Methods for Random Tessellations
TL;DR: In this article, the authors investigated the asymptotic properties of the typical cell by estimating the distribution tails of some of its geometric characteristics (inradius, volume, fundamental frequency).
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Extrapolation of Stationary Random Fields
TL;DR: This work introduces basic statistical methods for the extrapolation of stationary random fields and considers kriging extrapolation techniques for square integrable fields, and describes further extrapolation methods and discusses their properties.
References
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Book
Stochastic integration and differential equations
TL;DR: In this article, the authors propose a method for general stochastic integration and local times, which they call Stochastic Differential Equations (SDEs), and expand the expansion of Filtrations.
Book
Stochastic Geometry and Its Applications
TL;DR: Random Closed Sets I--The Boolean Model. Random Closed Sets II--The General Case.
Journal ArticleDOI
Stable non-Gaussian random processes , by G. Samorodnitsky and M. S. Taqqu. Pp. 632. £49.50. 1994. ISBN 0-412-05171-0 (Chapman and Hall).
Book
Lévy processes and infinitely divisible distributions
TL;DR: In this paper, the authors consider the distributional properties of Levy processes and propose a potential theory for Levy processes, which is based on the Wiener-Hopf factorization.
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