random scaling; Dirichlet process; Gaussian process; fractional Laplace motion; Brown-Resnick process; elliptical process; max-domain of attractions; tail asymptotics; Weibullian tails; second order extreme value conditions; max-stable distributions; conditional limiting theorems; Kotz approximation; asymptotic independence; Hüsler-Reiss triangular arrays; Dirichlet distributions; elliptical distributions; ruin probability; missing values; maxima of Gaussian processes
Hashorva Enkelejd, Weng Zhichao (2015), Limit laws for maxima of contracted stationary Gaussian sequences, in Communications in Statistics - Theory and Methods
, 44, 4641-4641.
Engelke Sebastian, Kabluchko Zakhar, Schlather Martin (2015), Maxima of independent, non-identically distributed Gaussian vectors, in Bernoulli
, 21(1), 38-61.
Hashorva Enkelejd, Li Jinzhu (2014), ASYMPTOTICS FOR A DISCRETE-TIME RISK MODEL WITH THE EMPHASIS ON FINANCIAL RISK, in PROBABILITY IN THE ENGINEERING AND INFORMATIONAL SCIENCES
, 28(4), 573-588.
Hashorva E., Ling C., Peng Z. (2014), Second-order tail asymptotis of deflated risks, in Insurance: Mathematics & Economics
, 56, 88-101.
Hashorva Enkelejd, Weng Zichao (2014), Tail asymptotic of Weibull-type risks., in Statistics
, 48(5), 1155-1165.
Merz M., Wüthrich M.V., Hashorva E. (2013), Dependence modelling in multivariate claims run-off triangles, in Annals of Actuarial Science
, 7(1), 3-25.
Yang Y., Hashorva E. (2013), Extremes and products of multivariate AC-product risks, in Insurance: Mathematics and Economics
, 52(2), 312-319.
Hashorva E, Macci C, Pacchiarotti B (2013), Large deviations for proportions of observations which fall in random sets determined by order statistics, in Methodology and Computing in Applied Probability
, 15(4), 875-896.
Hashorva Enkelejd, Weng Zhichao (2013), Limit laws for extremes of dependent stationary Gaussian arrays, in Statistics and Probability, Letters
, 83, 320-330.
Hashorva Enkelejd (2013), Minima and maxima of elliptical triangular arrays and spherical processes, in Bernoulli
, 19(3), 886-904.
Balakrishnan N, Hashorva E (2013), Scale mixtures of Kotz–Dirichlet distributions, in J. Multivariate Analysis
, 113, 48-58.
Hashorva E, Jaworski P (2012), Gaussian approximation of conditional elliptical copulas, in Journal Multivariate Analysis
, 111, 397-407.
Peng Z, Tong J.J., Weng Z. (2012), Joint limit distributions of exceedances point processes and partial sums of gaussian vector sequence, in Acta Mathematica Sinica, English Series
, 28(8), 1647-1662.
Hashorva Enkelejd, Ji Lanpeng, Tan Zhongquan (2012), On the infinite sums of deflated Gaussian products, in Electron. Commun. Probab.
, (17), 1-8.
Constantinescu C, Hashorva E, Ji L (2011), Archimedean copulas in finite and infinite dimensions-with application to ruin problems, in Insurance: Mathematics and Economics
, 49(3), 487-495.
This project aims to investigate the extremal behaviour of some important discrete and continuous random scaling models. Two canonical instances of random elements defined by random scaling are the Gaussian and the Dirichlet processes. Typically, random scaling models the presence of deflators or inflators in finance and insurance, the impact of measurement errors, missing values or latent shocks in statistics, or the influence of random time deformations for certain stochastic processes. The tractability of random scaling models and their natural emergence explains their wide applicability in statistics, finance and insurance, stochastic geometry, stochastic analysis, or physics.Recent research has shown that certain conditional limit theorems, tail approximation of Dirichlet distributions, asymptotic independence of polar random vectors, the extremal behaviour of specific aggregated risks, or the asymptotics of the maxima of elliptical processes are direct consequences of the underlying scaling phenomena.On the statistical side, the study of random scaling models paves new ways for estimating rare events influenced by large scaling effects, as well as for dealing with diverse patterns of missing observations.By relying on new asymptotic techniques and recent progress of extreme value theory this projects investigates the extremal properties of different random scaling models envisaging novel applications and theoretical results related to ruin theory, risk management, and extreme value theory.Another direction of the project with emphasis on theoretical results explores the effect of random scaling on the maxima and minima of elliptical and related stochastic processes, and studies the asymptotics of the maximum of those processes over random time intervals.