88,405 research outputs found
Local Stability of the Free Additive Convolution
We prove that the system of subordination equations, defining the free
additive convolution of two probability measures, is stable away from the edges
of the support and blow-up singularities by showing that the recent smoothness
condition of Kargin is always satisfied. As an application, we consider the
local spectral statistics of the random matrix ensemble , where is
a Haar distributed random unitary or orthogonal matrix, and and are
deterministic matrices. In the bulk regime, we prove that the empirical
spectral distribution of concentrates around the free additive
convolution of the spectral distributions of and on scales down to
.Comment: Third version: More details added to Lemma 6.3 and proof of Theorem
2.
New stochastic processes to model interest rates : LIBOR additive processes
In this paper, a new kind of additive process is proposed. Our main goal is to define,
characterize and prove the existence of the LIBOR additive process as a new stochastic process.
This process will be de.ned as a piecewise stationary process with independent increments,
continuous in probability but with discontinuous trajectories, and having "cà dlà g" sample paths.
The proposed process is specifically designed to derive interest-rates modelling because it
allows us to introduce a jump-term structure as an increasing sequence of Lévy measures. In
this paper we characterize this process as a Markovian process with an infinitely divisible,
selfsimilar, stable and self-decomposable distribution. Also, we prove that the Lévy-Khintchine
characteristic function and Lévy-Itô decomposition apply to this process. Additionally we
develop a basic framework for density transformations. Finally, we show some examples of
LIBOR additive processes
Multifractal analysis of the irregular set for almost-additive sequences via large deviations
In this paper we introduce a notion of free energy and large deviations rate
function for asymptotically additive sequences of potentials via an
approximation method by families of continuous potentials. We provide estimates
for the topological pressure of the set of points whose non-additive sequences
are far from the limit described through Kingman's sub-additive ergodic theorem
and give some applications in the context of Lyapunov exponents for
diffeomorphisms and cocycles, and Shannon-McMillan-Breiman theorem for Gibbs
measures.Comment: 23 pages, to appear in Nonlinearity; small changes made according to
comments from the referee
Finitely additive extensions of distribution functions and moment sequences: The coherent lower prevision approach
We study the information that a distribution function provides about the finitely additive probability measure inducing it. We show that in general there is an infinite number of finitely additive probabilities associated with the same distribution function. Secondly, we investigate the relationship between a distribution function and its given sequence of moments. We provide formulae for the sets of distribution functions, and finitely additive probabilities, associated with some moment sequence, and determine under which conditions the moments determine the distribution function uniquely. We show that all these problems can be addressed efficiently using the theory of coherent lower previsions
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