Remarks on the canonical representation of stationary linear symmetric α-stable processes (0<α<1)

1988 ◽  
pp. 464-473
Author(s):  
Yumiko Sato
Keyword(s):  
Canonical Representation ◽  
Stable Processes

scholarly journals On the determinism of the distributions of multiple Markov non-Gaussian symmetric stable processes

1998 ◽  
Vol 150 ◽  
pp. 177-196
Author(s):  
Katsuya Kojo
Keyword(s):  
Canonical Representation ◽  
Stable Processes ◽  
Symmetric Stable Processes ◽  
Non Gaussian

Abstract.Consider a non-Gaussian SαS process X = {X(t); t ∈ T} which is expressed as a canonical representation , and is continuous in probability. If X is n-ple Markov, then X has determinism of dimension n + 1. That is, any SαS process having the same (n + l)-dimensional distributions with X is identical in law with X.

Population dynamics driven by truncated stable processes with Markovian switching

2021 ◽  
Vol 58 (2) ◽  
pp. 505-522
Author(s):  
Zhenzhong Zhang ◽  
Jinying Tong ◽  
Qingting Meng ◽  
You Liang
Keyword(s):  
Population Dynamics ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Markovian Switching ◽  
Stable Processes ◽  
Necessary And Sufficient ◽  
The Impact

AbstractWe focus on the population dynamics driven by two classes of truncated $\alpha$-stable processes with Markovian switching. Almost necessary and sufficient conditions for the ergodicity of the proposed models are provided. Also, these results illustrate the impact on ergodicity and extinct conditions as the parameter $\alpha$ tends to 2.

scholarly journals A generalization of Matérn hard-core processes with applications to max-stable processes

2020 ◽  
Vol 57 (4) ◽  
pp. 1298-1312
Author(s):  
Martin Dirrler ◽  
Christopher Dörr ◽  
Martin Schlather
Keyword(s):  
Point Process ◽  
Point Processes ◽  
Hard Core ◽  
Domain Of Attraction ◽  
Stable Processes ◽  
Poisson Point Processes ◽  
Original Process ◽  
Mixed Moving Maxima

AbstractMatérn hard-core processes are classical examples for point processes obtained by dependent thinning of (marked) Poisson point processes. We present a generalization of the Matérn models which encompasses recent extensions of the original Matérn hard-core processes. It generalizes the underlying point process, the thinning rule, and the marks attached to the original process. Based on our model, we introduce processes with a clear interpretation in the context of max-stable processes. In particular, we prove that one of these processes lies in the max-domain of attraction of a mixed moving maxima process.

scholarly journals Unbounded Wiener–Hopf Operators and Isomorphic Singular Integral Operators

2021 ◽  
Vol 15 (3) ◽  
Author(s):  
Domenico P. L. Castrigiano
Keyword(s):  
Singular Integral ◽  
Polar Decomposition ◽  
Integral Operators ◽  
Canonical Representation ◽  
Friedrichs Extension ◽  
Finite Dimensional ◽  
Transformation Type ◽  
Rational Symbols ◽  
Shift Invariance ◽  
Densely Defined

AbstractSome basics of a theory of unbounded Wiener–Hopf operators (WH) are developed. The alternative is shown that the domain of a WH is either zero or dense. The symbols for non-trivial WH are determined explicitly by an integrability property. WH are characterized by shift invariance. We study in detail WH with rational symbols showing that they are densely defined, closed and have finite dimensional kernels and deficiency spaces. The latter spaces as well as the domains, ranges, spectral and Fredholm points are explicitly determined. Another topic concerns semibounded WH. There is a canonical representation of a semibounded WH using a product of a closable operator and its adjoint. The Friedrichs extension is obtained replacing the operator by its closure. The polar decomposition gives rise to a Hilbert space isomorphism relating a semibounded WH to a singular integral operator of Hilbert transformation type. This remarkable relationship, which allows to transfer results and methods reciprocally, is new also in the thoroughly studied case of bounded WH.

Practical Tools for Reasoning About Linear Constraints

1991 ◽  
Vol 15 (3-4) ◽  
pp. 357-379
Author(s):  
Tien Huynh ◽  
Leo Joskowicz ◽  
Catherine Lassez ◽  
Jean-Louis Lassez
Keyword(s):  
Logic Programming ◽  
Intelligent Systems ◽  
Optimization Problem ◽  
Spatial Reasoning ◽  
Quantifier Elimination ◽  
Canonical Representation ◽  
Linear Constraints ◽  
Practical Applications ◽  
Variable Elimination ◽  
Fourier Algorithm

We address the problem of building intelligent systems to reason about linear arithmetic constraints. We develop, along the lines of Logic Programming, a unifying framework based on the concept of Parametric Queries and a quasi-dual generalization of the classical Linear Programming optimization problem. Variable (quantifier) elimination is the key underlying operation which provides an oracle to answer all queries and plays a role similar to Resolution in Logic Programming. We discuss three methods for variable elimination, compare their feasibility, and establish their applicability. We then address practical issues of solvability and canonical representation, as well as dynamical updates and feedback. In particular, we show how the quasi-dual formulation can be used to achieve the discriminating characteristics of the classical Fourier algorithm regarding solvability, detection of implicit equalities and, in case of unsolvability, the detection of minimal unsolvable subsets. We illustrate the relevance of our approach with examples from the domain of spatial reasoning and demonstrate its viability with empirical results from two practical applications: computation of canonical forms and convex hull construction.

scholarly journals Yaglom limit for stable processes in cones

2018 ◽  
Vol 23 (0) ◽  
Author(s):  
Krzysztof Bogdan ◽  
Zbigniew Palmowski ◽  
Longmin Wang
Keyword(s):  
Stable Processes ◽  
Yaglom Limit
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