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Symmetric jump processes : localization, heat kernels and convergence

Richard F. Bass, Moritz Kassmann, Takashi Kumagai (2010)

Annales de l'I.H.P. Probabilités et statistiques

We consider symmetric processes of pure jump type. We prove local estimates on the probability of exiting balls, the Hölder continuity of harmonic functions and of heat kernels, and convergence of a sequence of such processes.

Symmetric models for lifetimes: the role of exchangeable equivalence relations

Anna Gerardi, Barbara Torti (2003)

Bollettino dell'Unione Matematica Italiana

A model of a heterogeneous population partitioned into a finite number of classes according an exchangeable equivalence relation is studied. With this motivation the properties of exchangeable equivalence relations are investigated and, in particular, the structure of its equivalence classes is characterized.

Symmetric partitions and pairings

Ferenc Oravecz (2000)

Colloquium Mathematicae

The lattice of partitions and the sublattice of non-crossing partitions of a finite set are important objects in combinatorics. In this paper another sublattice of the partitions is investigated, which is formed by the symmetric partitions. The measure whose nth moment is given by the number of non-crossing symmetric partitions of n elements is determined explicitly to be the "symmetric" analogue of the free Poisson law.

Symmetries of random discrete copulas

Arturo Erdely, José M. González–Barrios, Roger B. Nelsen (2008)

Kybernetika

In this paper we analyze some properties of the discrete copulas in terms of permutations. We observe the connection between discrete copulas and the empirical copulas, and then we analyze a statistic that indicates when the discrete copula is symmetric and obtain its main statistical properties under independence. The results obtained are useful in designing a nonparametric test for symmetry of copulas.

Symmetrization of probability measures, pushforward of order 2 and the Boolean convolution

Wojciech Młotkowski, Noriyoshi Sakuma (2011)

Banach Center Publications

We study relations between the Boolean convolution and the symmetrization and the pushforward of order 2. In particular we prove that if μ₁,μ₂ are probability measures on [0,∞) then ( μ ₁ ⨄ μ ₂ ) s = μ ₁ s ⨄ μ ₂ s and if ν₁,ν₂ are symmetric then ( ν ₁ ⨄ ν ₂ ) ( 2 ) = ν ₁ ( 2 ) ⨄ ν ₂ ( 2 ) . Finally we investigate necessary and sufficient conditions under which the latter equality holds.

Systemic risk through contagion in a core-periphery structured banking network

Oliver Kley, Claudia Klüppelberg, Lukas Reichel (2015)

Banach Center Publications

We contribute to the understanding of how systemic risk arises in a network of credit-interlinked agents. Motivated by empirical studies we formulate a network model which, despite its simplicity, depicts the nature of interbank markets better than a symmetric model. The components of a vector Ornstein-Uhlenbeck process living on the nodes of the network describe the financial robustnesses of the agents. For this system, we prove a LLN for growing network size leading to a propagation of chaos result....

Systems of dyadic cubes in a doubling metric space

Tuomas Hytönen, Anna Kairema (2012)

Colloquium Mathematicae

A number of recent results in Euclidean harmonic analysis have exploited several adjacent systems of dyadic cubes, instead of just one fixed system. In this paper, we extend such constructions to general spaces of homogeneous type, making these tools available for analysis on metric spaces. The results include a new (non-random) construction of boundedly many adjacent dyadic systems with useful covering properties, and a streamlined version of the random construction recently devised by H. Martikainen...

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