Like most results in information theory, the classical Slepian-Wolf theorem is asymptotic. We characterize how quickly the limits put forth by information theory can be reached. Our contribution is two-fold. First, we investigate the non-asymptotic regime for two binary sources that generate sequences with a symmetric joint distribution. Second, we provide tight converse and achievable bounds a...

We define a type of generalized asymptotic series called v-asymptotic. We show that every func­ tion with moderate growth at infinity has a v-asymptotic expansion. We also describe the set of v-asymptotic series, where a given function with moderate growth has a unique v-asymptotic ex­ pansion. As an application to random matrix theory we calculate the coefficients and establish the uniqueness ...

The uniform asymptotic description of electromagnetic pulse propagation in a single-resonance Lorentz medium is presented. The modern asymptotic theory used here relies on Olver's saddle-point method [Stud. Appl. Math. Rev. 12, 228 (1970)] together with the uniform asymptotic theory of Handelsman and Bleistein [Arch. Ration. Mech. Anal. 35, 267 (1969)] when two saddle points are at infinity (fo...

We consider asymptotic properties of curve-crossing counts of linear processes and nonlinear time series by curves. Central limit theorems are obtained for curve-crossing counts of short-range dependent processes. For the long-range dependence case, the asymptotic distributions are shown to be either multiple Wiener–Itô integrals or integrals with respect to stable Lévy processes, depending on ...

Let A be an n × n subgaussian matrix (entries are i.i.d. subgaussian r.v’s with variance 1). There are two reasons for the invertibility of A, depending on the nature of the unit vector on which A is acting – either compressible or incompressible. We recall that compressible vectors are those whose distance is at most some constant ρ from the set of (δn)-sparse vectors, and incompressible vecto...

This paper investigates the asymptotic theory for a factor GARCH model. Sufficient conditions for strict stationarity, existence of certain moments, geometric ergodicity and βmixing with exponential decay rates are established. These conditions allow for volatility spill-over and integrated GARCH. We then show the strong consistency and asymptotic normality of the quasi-maximum likelihood estim...

A description of the Kasparov group KK(A,B) is given in terms of Cuntz pairs of representations and the notion of proper asymptotic unitary equivalence that we introduce here. The use of the word ‘proper’ reflects the crucial fact that all unitaries implementing the equivalence can be chosen to be compact perturbations of identity. The result has significant applications to the classification t...

1 Definition The topic in this lecture is Subgaussian random variables. We start with the definition, and discuss some properties they hold. Definition 1 (Subgaussian random variables). A random variable X is subgaussian if ∃c, C such that P(|x| > t) ≤ Ce −ct 2 ∀t ≥ 0. (1) As the name suggests, the notion of subgaussian random variables is a generalization of Gaussian random variables. Both the...

In Bayesian decision theory, it is known that robustness with respect to the loss and the prior can be improved by adding new observations. In this article we study the rate of robustness improvement with respect to the number of observations n. Three usual measures of posterior global robustness are considered: the (range of the) Bayes actions set derived from a class of loss functions, the ma...