1,468 research outputs found
On a method of introducing free-infinitely divisible probability measures
Random integral mappings give isomorphisms between the
sub-semigroups of the classical and the free-infinite divisible
probability measures. This allows us to introduce new examples
of such measures and their corresponding characteristic functionals.Comment: 16 page
Gibbs states over the cone of discrete measures
We construct Gibbs perturbations of the Gamma process on \mathbbm{R}^d,
which may be used in applications to model systems of densely distributed
particles. First we propose a definition of Gibbs measures over the cone of
discrete Radon measures on \mathbbm{R}^d and then analyze conditions for
their existence. Our approach works also for general L\'evy processes instead
of Gamma measures. To this end, we need only the assumption that the first two
moments of the involved L\'evy intensity measures are finite. Also uniform
moment estimates for the Gibbs distributions are obtained, which are essential
for the construction of related diffusions. Moreover, we prove a Mecke type
characterization for the Gamma measures on the cone and an FKG inequality for
them.Comment: Keywords: Gamma process, Poisson point process, discrete Radon
measures, Gibbs states, DLR equation, Mecke identity, FK
Exact asymptotic for distribution densities of Levy functionals
A version of the saddle point method is developed, which allows one to
describe exactly the asymptotic behavior of distribution densities of Levy
driven stochastic integrals with deterministic kernels. Exact asymptotic
behavior is established for (a) the transition probability density of a
real-valued Levy process; (b) the transition probability density and the
invariant distribution density of a Levy driven Ornstein-Uhlenbeck process; (c)
the distribution density of the fractional Levy motion.Comment: Revised versio
Modeling self-organization in pedestrians and animal groups from macroscopic and microscopic viewpoints
This paper is concerned with mathematical modeling of intelligent systems,
such as human crowds and animal groups. In particular, the focus is on the
emergence of different self-organized patterns from non-locality and anisotropy
of the interactions among individuals. A mathematical technique by
time-evolving measures is introduced to deal with both macroscopic and
microscopic scales within a unified modeling framework. Then self-organization
issues are investigated and numerically reproduced at the proper scale,
according to the kind of agents under consideration.Comment: 24 pages, 13 figure
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