• We review the current state of statistical modeling of asymptotically independent data. Our discussion includes necessary and sufficient conditions for asymptotic independence, results on the asymptotic independence of statistics of interest, estimation and inference issues, joint tail modeling, and conditional approaches. For each of these topics we give an account of existing approaches and...

Abstract In this paper, we study the asymptotic behavior of an $\varepsilon $ ε -periodic 3D stable structure made beams circular cross-section radius $r$ r when periodicity parameter and ratio ${r/\varepsilon }$ / simultaneously tend to 0. The analysis is performed within fr...

Department of Mathematical Statistics and Actuarial Science University of Bern, Sidlerstrasse 5 CH-3012 Bern, Switzerland October 8, 2008 Abstract: Let (S1, S2) = (R cos(Θ), R sin(Θ)) be a bivariate random vector with associated random radius R which has distribution function F being further independent of the random angle Θ. In this paper we investigate the asymptotic behaviour of the conditio...

We study in depth the properties of the GARCH(1,1) model and the assumptions on the parameter space under which the process is stationary. In particular, we prove ergodicity and strong stationarity for the conditional variance (squared volatility) of the process. We show under which conditions higher order moments of the GARCH(1,1) process exist and conclude that GARCH processes are heavy-taile...

In this work, we give sharp asymptotic equivalents in the limit $h\to 0$ of small eigenvalues Witten Laplacian, that is operator associated with quadratic form $$ \psi\in H^1_0(\Omega)\mapsto h^2 \int_\Omega \big \vert \nabla (e^{\frac 1hf} \psi\big )\big \vert^2\, e^{-\frac 2hf},$$where $\overline\Omega=\Omega\cup \partial \Omega$ an oriented $C^\infty$ compact and connected Riemannian manifol...