292 research outputs found
Functional central limit theorems on Lie groups: A survey
The general solution of the functional central limit problems for triangular arrays of
random variables with values in a Lie group is described. The role of processes of finite
variation is clarified. The special case of processes with independent increments having
Markov generator is treated. Connections with Hille–Yosida theory for two–parameter
evolution families of operators and with the martingale problem are explained
Fourier transform of a Gaussian measure on the Heisenberg group
An explicit formula is derived for the Fourier transform of a Gaussian
measure on the Heisenberg group at the Schrodinger representation. Using this
explicit formula, necessary and sufficient conditions are given for the
convolution of two Gaussian measures to be a Gaussian measure.Comment: 38 pages, completed versio
On convergence properties of infinitesimal generators of scaled multi-type CBI processes
It is a common method for proving weak convergence of a sequence of
time-homogeneous Markov processes towards a time-homogeneous Markov process
first to show convergence of the corresponding infinitesimal generators and
then to check some additional conditions. The aim of the present paper is to
investigate convergence properties of discrete infinitesimal generators of
appropriately scaled random step functions formed from a multi-type continuous
state and continuous time branching process with immigration. We also present a
convergence result for usual infinitesimal generators of the branching
processes in question appropriately normalized.Comment: 17 pages. Title is changed, and new parts (e.g., Corollary 3.5 and
Remark 3.6) are added. In Section 2 we recall some notions and statements
from arXiv:1403.0245 and arXiv:1404.224
Asymptotic behavior of critical irreducible multi-type continuous state and continuous time branching processes with immigration
Under natural assumptions, a Feller type diffusion approximation is derived
for critical, irreducible multi-type continuous state and continuous time
branching processes with immigration. Namely, it is proved that a sequence of
appropriately scaled random step functions formed from a critical, irreducible
multi-type continuous state and continuous time branching process with
immigration converges weakly towards a squared Bessel process supported by a
ray determined by the Perron vector of a matrix related to the branching
mechanism of the branching process in question.Comment: 29 pages. In Section 2 we recall some notions and statements from
arXiv:1403.024
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