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We study the extremal behavior of a stochastic integral driven by a multivariate Lévy process that is regularly varying with index α > 0. For predictable integrands with a finite (α+ δ)-moment, for some δ > 0, we show that the extremal behavior of the stochastic integral is due to one big jump of the driving Lévy process and we determine its limit measure(More)
In this paper we clarify dependence properties of elliptical distributions by deriving general but explicit formulas for the coefficients of upper and lower tail dependence and spectral measures with respect to different norms. We show that an elliptically distributed random vector is regularly varying if and only if the bivariate marginal distributions(More)
The foundations of regular variation for Borel measures on a complete separable space S, that is closed under multiplication by nonnegative real numbers, is reviewed. For such measures an appropriate notion of convergence is presented and the basic results such as a Portmanteau theorem, a mapping theorem and a characterization of relative compactness are(More)
A random vector X with representation X = ∑ j≥0 AjZj is considered. Here, (Zj) is a sequence of independent and identically distributed random vectors and (Aj) is a sequence of random matrices, ‘predictable’ with respect to the sequence (Zj). The distribution of Z1 is assumed to be multivariate regular varying. Moment conditions on the matrices (Aj) are(More)
Within-die process variations arise during integrated circuit (IC) fabrication in the sub-100nm regime. These variations are of paramount concern as they deviate the performance of ICs from their designers' original intent. These deviations reduce the parametric yield and revenues from integrated circuit fabrication. In this paper we provide a complete(More)
We extend classical results by A. V. Nagaev [Izv. Akad. Nauk UzSSR Ser. Fiz.–Mat. Nauk 6 (1969) 17–22, Theory Probab. Appl. 14 (1969) 51–64, 193–208] on large deviations for sums of i.i.d. regularly varying random variables to partial sum processes of i.i.d. regularly varying vectors. The results are stated in terms of a heavy-tailed large deviation(More)
In some recent papers (Elliott and van der Hoek, 2003; Hu and Øksendal, 2003) a fractional Black-Scholes model have been proposed as an improvement of the classical Black-Scholes model (see also Benth, 2003; Biagini et al., 2002; Biagini and Øksendal, 2004). Common to these fractional BlackScholes models, is that the driving Brownian motion is replaced by a(More)
In many applications involving functional large deviations for partial sums of stationary, but not iid, processes with heavy tails, a curious phenomenon arises: closely grouped together large jumps coalesce together in the limit, leading to loss of information of the order in which these jumps arrive. In particular, many functionals of interest become(More)