We introduce a new micro-macro decomposition of collisional kinetic equations in the specific case of the diffusion limit, which naturally incorporates the incoming boundary conditions. The idea is to write the distribution function f in all its domain as the sum of an equilibrium adapted to the boundary (which is not the usual equilibrium associated with f) and a remaining kinetic part. This e...

Classical Edgeworth expansions provide asymptotic correction terms to the Central Limit Theorem (CLT) up to an order that depends on the number of moments available. In this paper, we provide subsequent correction terms beyond those given by a standard Edgeworth expansion in the general case of regularly varying distributions with diverging moments (beyond the second). The subsequent terms can ...

A simple scheme is presented for modifying geometric moments to use geodesic distances. This provides a set of global shape descriptors that are invariant to bending as well as rotation, translation and scale.

Abstract. This paper considers the timeand space-dependent linear Boltzmann equation with general boundary conditions in the case of inelastic (granular) collisions. First, in the (angular) cut-off case, mild L1-solutions are constructed as limits of the iterate functions and boundedness of higher velocity moments are discussed in the case of inverse power collisions forces. Then the problem of...

flood frequency analysis is faced with the problem of data and information limitation in arid and semi-arid regions. particularly in these regions, the length of records is usually too short to ensure reliable quantile estimates. more than 75% of iran is located in arid and semi-arid regions and despite the low annual precipitation, often large floods occur. one way to provide more information ...

We show, by the method of cumulants, that checking whether the central limit theorem for sums of Wick powers of a stationary sequence holds can be reduced to the study of an associated graph problem (see Corollary 1). We obtain thus central limit theorems under various integrability conditions on the cumulant spectral functions (Theorems 2, 3). 1 A. Introduction. Let X¡ be a zero mean stationar...

This work obtains sharp closed-form exponential concentration inequalities of Bernstein type for the ubiquitous beta distribution, improving upon sub-Gaussian and sub-gamma bounds previously studied in this context. The proof leverages a novel handy recursion order 2 central moments obtained from hypergeometric representations moments; is useful obtaining explicit expressions various tail appro...

We prove the almost sure central limit theorem for martingales via an original approach which uses the Carleman moment theorem together with the convergence of moments of martingales. Several statistical applications to autoregressive and branching processes are also provided.

We use combinatorial optimisation to accumulate strokes into digits. The recognition hierarchy is novel in that it is not crafted to be a “good” representation scheme, but is generated from the repeated calculation of low-order central moments.