36 citations · 80 across the 15 of their papers we have counts for
11 papers · 1 filter
Aggregating heavy-tailed random vectors: from finite sums to Lévy processes
Bikramjit Das, Vicky Fasen-Hartmann
The tail behavior of aggregates of heavy-tailed random vectors is known to be determined by the so-called principle of "one large jump'', be it for finite sums, random sums, or, Lé…
Growth of Common Friends in a Preferential Attachment Model
Bikramjit Das, Souvik Ghosh
The number of common friends (or connections) in a graph is a commonly used measure of proximity between two nodes. Such measures are used in link prediction algorithms and recomme…
Tail probabilities of random linear functions of regularly varying random vectors
Bikramjit Das, Vicky Fasen-Hartmann, Claudia Klüppelberg
We provide a new extension of Breiman's Theorem on computing tail probabilities of a product of random variables to a multivariate setting. In particular, we give a complete charac…
Hidden regular variation, copula models, and the limit behavior of conditional excess risk measures
Bikramjit Das, Vicky Fasen-Hartmann
Risk measures like Marginal Expected Shortfall and Marginal Mean Excess quantify conditional risk and in particular, aid in the understanding of systemic risk. In many such scenari…
Risk concentration under second order regular variation
Bikramjit Das, Marie Kratz
Measures of risk concentration and their asymptotic behavior for portfolios with heavy-tailed risk factors is of interest in risk management. Second order regular variation is a st…
Heavy-tailed random walks, buffered queues and hidden large deviations
Harald Bernhard, Bikramjit Das
It is well-known that large deviations of random walks driven by independent and identically distributed heavy-tailed random variables are governed by the so-called principle of on…
Generation and Detection of Multivariate Regular Variation and Hidden Regular Variation
Bikramjit Das, Sidney Resnick
We review definitions of multivariate regular variation (MRV) and hidden regular variation (HRV) for distributions of random vectors and then summarize methods for generating model…
Extremal behavior of squared Bessel processes attracted by the Brown-Resnick process
Bikramjit Das, Sebastian Engelke, Enkelejd Hashorva
The convergence of properly time-scaled and normalized maxima of independent standard Brownian motions to the Brown-Resnick process is well-known in the literature. In this paper,…
Living on the multi-dimensional edge: seeking hidden risks using regular variation
Bikramjit Das, Abhimanyu Mitra, Sidney Resnick
Multivariate regular variation plays a role assessing tail risk in diverse applications such as finance, telecommunications, insurance and environmental science. The classical theo…
Conditioning on an extreme component: Model consistency with regular variation on cones
Bikramjit Das, Sidney I. Resnick
Multivariate extreme value theory assumes a multivariate domain of attraction condition for the distribution of a random vector. This necessitates that each component satisfies a m…
QQ plots, Random sets and data from a heavy tailed distribution
Bikramjit Das, Sidney I. Resnick
The QQ plot is a commonly used technique for informally deciding whether a univariate random sample of size n comes from a specified distribution F. The QQ plot graphs the sample q…