A fast method for estimating the parameters of a stable-APARCH not requiring likelihood or iteration is proposed. Several powerful tests for the (asymmetric) stable Paretian distribution with tail index 1 ă α ă 2 are used for assessing the appropriateness of the stable assumption as the innovations process in stable-GARCH-type models for daily stock returns. Overall, there is strong evidence ag...

✐ ă " […] Karma is not about immediate retribution but rather about the impossibility of ultimately escaping the consequences of our own actions […] " ― Hindu and Buddhist saying

We proved that a finite commuting Boyd-Wong type contractive family with equicontinuous words have the approximate common fixed point property. We also proved that given X Ă R, compact and convex subset, F : X Ñ X a compact-and-convex valued Lipschitz correspondence and g an isometry on X, then gF “ F g implies F admits a Lipschitz selection commuting with g.

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Lu :“ ́ε4u` fpx, y;uq “ 0 for px, yq P Ω, u “ 0 on BΩ, (1.1) posed in a, possibly non-Lipschitz, polygonal domain Ω Ă R. Here 0 ă ε ď 1. We also assume that f is continuous on ΩˆR and satisfies fp ̈; sq P L8pΩq for all s P R, and the one-sided Lipschitz condition fpx, y;uq ́ fpx, y; vq ě Cf ru ́ vs whenever u ě v, with some constant Cf ě 0. Then there is a unique solution u PW 2 ` pΩq ĎW 1 q Ă CpΩ̄q...

In this work we prove that the set of points at infinity S8 :“ ClRPm pSqXH8 of a semialgebraic set S Ă R that is the image of a polynomial map f : R Ñ R is connected. This result is no longer true in general if f is a regular map. However, it still works for a large family of regular maps that we call quasi-polynomial maps.

Given k collections of 2SAT clauses on the same set of variables V , can we find one assignment that satisfies a large fraction of clauses from each collection? We consider such simultaneous constraint satisfaction problems, and design the first nontrivial approximation algorithms in this context. Our main result is that for every CSP F , for k ă Õplog1 nq, there is a polynomial time constant f...

Abstract. We consider the model Yi “ XiUi, i “ 1, . . . , n, where the Xi, the Ui and thus the Yi are all independent and identically distributed. The Xi have density f and are the variables of interest, the Ui are multiplicative noise with uniform density on r1 ́ a, 1` as, for some 0 ă a ă 1, and the two sequences are independent. However, only the Yi are observed. We study nonparametric estima...

The corresponding topology is called norm-topology. The norm-topology naturally gives rise to the concept of convergence and continuity. A sequence txnun“1 Ă X is said to converge to x in the norm-metric, or strongly, if }xn ́ x} Ñ 0 as nÑ 8. A function f : X Ñ Y , where Y is a topological space, is continuous if fpxnq Ñ fpxq whenever xn Ñ x, or equivalently, if f ́1pUq is open for any open U Ă Y...