Sanov Property, Generalized $I$-Projection and a Conditional Limit Theorem

The Local Limit Theorem: A Historical Perspective

The local limit theorem describes how the density of a sum of random variables follows the normal curve. However the local limit theorem is often seen as a curiosity of no particular importance when compared with the central limit theorem. Nevertheless the local limit theorem came first and is in fact associated with the foundation of probability theory by Blaise Pascal and Pierre de Fer...

A Weak Limit Theorem for Generalized Jiřina Processes

In this paper we prove that a sequence of scaled generalized Jiřina processes can converge weakly to a nonlinear diffusion process with Lévy jumps under certain conditions.

Single Valued Extension Property and Generalized Weyl’s Theorem

Let T be an operator acting on a Banach space X, let σ(T ) and σBW (T ) be respectively the spectrum and the B-Weyl spectrum of T . We say that T satisfies the generalized Weyl’s theorem if σBW (T ) = σ(T ) \E(T ), where E(T ) is the set of all isolated eigenvalues of T . The first goal of this paper is to show that if T is an operator of topological uniform descent and 0 is an accumulation poi...

Generalized Central Limit Theorem and Extreme Value Statistics

A projection property for buildings

There are two motivations for studying the question whether X has the projection property. Firstly, Arrow's \dictator theorem" states that the only maps of a product X A to X with certain properties are the projections (see A], PRS]). Secondly, the projection property is closely related to the xed point property (see C]). For a detailed discussion of the projection property, its background and ...