Extreme values ; Seleznjev Theorem; Interpolation of random fields; Conditional Gaussian process; Time discretisation of random fields; Perturbed risk process; Gaussian random field; Storage process; Shepp statistics; Chi-square process; Limit theorems for Gaussian processes; Weak and strong dependence; Locally-stationary random field
Liu Peng, Zhang Chunsheng, Ji Lanpeng (2017), A note on ruin problems in perturbed classical risk models, in Statistics and Probability Letters
, 120, 28-33.
Asimit V, Hashorva E, Kortschak D (2017), Aggregation of randomly weighted large risks, in IMA J Management Math
, 28(3), 403-419.
Engelke S, Kabluchko Z. (2016), A characterization of the normal distribution using stationary max-stable processes, in Extremes
, 19(1), 1-6.
Engelke S., Ivanovs J. (2016), A Levy process on the real line seen from its supremum and max-stable processes, in Electronic J. Probabiliy
, 21(paper no. ), 1-19.
Dombry C., Engelke S., Oesting M. (2016), Exact simulation of max-stable processes, in Biometrika
, 106, 303-317.
Hashorva E., Ji L. (2016), Extremes of -locally stationary Gaussian random fields, in Transactions of American Mathematica Soc.
, 368(1), 1-26.
Debicki K., Hashorva E., Ji L. (2016), Extremes of a class of non-homogeneous Gaussian random fields, in Annals of Probability
, 44(2), 984-1012..
Liu Peng, Ji Lanpeng (2016), Extremes of Chi-square Processes with trend, in Probability and Mathematical Statistics
, 36(1), 1-20.
Debicki K., Liu P. (2016), Extremes of stationary Gaussian storage models, in Extremes
, 19(2), 273-302.
Asadi P, Davision A, Engelke S (2016), Extremes on river networks, in Annals of Applied Statistics
, 9(4), 2023-2050.
Hashorva E, Peng Z, Weng Z (2016), Higher-order expansions of distributions of maxima in a Hüsler-Reiss model, in Methodology and Computing in Applied Probability
, 18(1), 181-196.
Hashorva Enkelejd, Ling Chengxiu (2016), Maxima of skew elliptical triangular arrays, in Communications in Statistics - Theory and Methods
, 45(12), 3692-3705.
Tan Z., Ling C. (2016), On maxima of chi-processes over threshold dependent grids, in Statistics: A Journal of Theoretical and Applied Statistics
, 50(3), 579-595.
Debicki K., Hashorva E., Ji L. (2016), On Parisian ruin over a finite-time horizon, in Science China Mathematics
, 59(3), 557-572.
Ling Chengxiu, Peng Zuoxiang (2016), Tail asymptotics of generalized deflated risks with insurance applications, in Insurance Mathematics & Economics
, 71, 220-231.
Hashorva E., Lifshits M., Seleznjev O. (2015), Approximation of a random process with variable smoothness, in Hallin M. (ed.), Springer Verlag, Germany, 189-208.
Hashorva Enkelejd, Mishura Yulyia, Seleznjev Oleg (2015), Boundary non-crossing probabilities for fractional Brownian motion with trend, in Stochastics
, 87(6), 946-965.
Enkelke S., Malinovski A., Kabluchko Z., Schlather M. (2015), Estimation of Hüsler-Reiss distributions and Brown-Resnick processes, in Journal of the Royal Statistical Society B
, 77, 239-265.
Hashorva Enkelejd, Korshunov Dmitry, Piterbarg Vladimir I. (2015), Extremal Behavior of Gaussian Chaos via Probabilistic Approach, in Extremes
, 18(3), 315-347.
Das Bikram, Engelke Sebastian, Hashorva Enkelejd (2015), Extremal behavior of squared Bessel processes attracted by the Brown-Resnick process, in Stochastic Processes and their Applications
, 125(2), 780-796.
Enkelejd Hashorva (2015), Extremes of Aggregated Dirichlet Risks, in J. Multivariate Analysis
, 133, 334-345.
Dębicki K., Hashorva E., Soja-Kukieła N. (2015), Extremes of homogeneous Gaussian random fields, in Journal of Applied Probability
, 52(1), 55-67.
Debicki K., Hashorva E., Ji L., Ling C. (2015), Extremes of order statistics of stationary processes, in Test
, 24(2), 229-248.
Debicki K., Hashorva E., Ji L., Tabis K. (2015), Extremes of vector-valued Gaussian processes: Exact asymptotics, in Stochastic Proc Applications
, 125(11), 4039-4065.
Debicki K., Hashorva E., Ji L. (2015), Gaussian risk models with financial constraints, in Scandinavian Actuarial Journal
, 6, 469-481.
Hashorva Enkelejd, Peng Liang, Weng Zhichao (2015), Maxima of a triangular array of multivariate Gaussian sequence, in Statistics & Probability Letters
, 103, 62-72.
Engelke S., Kabluchko Z. (2015), Max-stable processes and stationary systems of Levy particles, in Stochastic Proc Applications
, 125(11), 4272-4299.
Korshunov Dmitry, Piterbarg Vladimir I., Hashorva Enkelejd (2015), On Laplace asymptotic method, with application to random chaos, in Matematicheskie Zametki
, 97(6), 868-883.
Hashorva E., Ratovomirija G (2015), On Sarmanov Mixed Erlang Risks in Insurance Applications, in ASTIN Bulletin
, 45(1), 175-205.
Peng L., Hashorva E., Ji L. (2015), On the gamma-reflected processes with fBm input, in Lithianian Math J.
, 55(3), 402-412.
Debicki K., Hashorva E., Ji L. (2015), Parisian ruin of self-similar Gaussian risk processes, in J. Applied Probability
, 53(3), 688-702.
Hashorva Enkelejd, Ji Lanpeng (2015), Piterbarg theorems for chi-processes with trend, in Extremes
Hashorva E., Tan Z. (2015), Piterbarg's max-discretisation theorem for stationary vector Gaussian processes observed on different grids, in Statistics
, 49(2), 338-360.
Farkas Julia, Hashorva Enkelejd (2015), Tail approximation for reinsurance portfolios of Gaussian-like risks, in Scandinavian Actuarial Journal
, 4, 319-331.
Hashorva Enkelejd, Li Jinzhu (2015), Tail Behaviour of Weighted Sums of Order Statistics of Dependent Risks, in Stochastic Models
, 31(1), 1-19.
Chengxiu Ling, Zuoxiang Peng (2015), Tail dependence for two skew slash distributions, in Statistics and Its Interface
, 8(1), 63-69.
Ling Chengxiu, Peng Zuoxiang (2015), Tail dependence for two skew slash distributions, in Statistics and its Interfaces
, 8(1), 63-69.
Hashorva Enkelejd, Ling Chengxiu, Peng Zuoxiang (2014), Tail asymptotic expansions for L-statisitcs., in Science China Mathematics
, 57(10), 1993-2012.
Ji Lanpeng, Zhang Chunsheng (2014), A duality result for the generalized Erlang risk model, in Risks
, 2, 456-466.
Embrechts P., Hashorva E., Mikosch T. (2014), Aggregation of log-linear risks, in J. Appl. Probab.
, 51(A), 203-212.
Hashorva Enkelejd, Ji Lanpeng (2014), Approximation of passage times of gamma-reflected processes with fBm input, in Journal of Applied Probability
, 51(3), 713-726.
Hashorva E, Li J (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 Enkelejd, Ji Lanpeng (2014), Asymptotics of the finite-time ruin probability for the Sparre Andersen risk model perturbed by an inflated stationary chi-process, in Communications in Statistics - Theory and Methods
, 43, 2540-2548.
Enkelejd Hashorva, Zhichao Weng (2014), Berman's inequality under random scaling, in Statistics and Its Interface
, 7(3), 339-349.
Hashorva E., Mishura Y. (2014), Boundary Non-Crossings of Additive Wiener Fields, in Lithuanian Math. J.
, 54(3), 277-289.
Hashorva Enkelejd, Ji Lanpeng (2014), EXTREMES AND FIRST PASSAGE TIMES OF CORRELATED FRACTIONAL BROWNIAN MOTIONS, in STOCHASTIC MODELS
, 30(3), 272-299.
Hashorva Enkelejd, Nadarajah Saralees, Pogany K Tibor (2014), Extremes of perturbed bivariate Rayleigh risks, in REVSTAT
, 12(1), 157-168.
Debicki K., Hashorva E., Ji L., Tan Z. (2014), Finite-time ruin probability of aggregate Gaussian processes, in Markov Processes and Related Fields
, 20, 435-450.
Debicki Krzysztof, Hashorva Enkelejd, Ji Lanpeng (2014), Gaussian approximation of perturbed chi-square risks, in Statistics and Its Interface
, 7(3), 363-373.
Hashorva Enkelejd, Peng Zuoxiang, Weng Zhichao (2014), Limit properties of exceedances point processes of scaled stationary Gaussian sequences, in Probability and Mathematical Statistics
, 34(1), 45-59.
Hashorva Enkelejd, Weng Zhichao (2014), Maxima and minima of complete and incomplete stationary sequences, in Stochastics An International Journal of Probability and Stochastic Processes
, 86(5), 707-720.
Hashorva Enkelejd, Ling Chengxiu, Peng Zuoxiang (2014), Modeling of Censored Bivariate Extremal Events, in Journal of the Korean Statistical Society
, 43(3), 323-338.
Tan Zhongquan, Hashorva Enkelejd (2014), On Piterbarg max-discretisation theorem for standardised maximum of stationary gaussian processes, in Methodology and Computing in Applied Probability
, 16(1), 169-185.
Debicki Krzysztof, Hashorva Enkelejd, Ji Lanpeng, Tabis Kamil (2014), On the probability of conjunctions of stationary Gaussian processes, in Statistics & Probability Letters
, 88, 141-148.
Hashorva Enkelejd, Ji Lanpeng (2014), Random shifting and scaling of insurance risks, in Risks
, 2, 277-288.
Kortschak Dominik, Hashorva Enkelejd (2014), Second order asymptotics of aggregated log-elliptical risk, in Methodology and Computing in Applied Probability
, 16(4), 969-985.
Hashorva Enkelejd, Kortschak Dominik (2014), Tail asymptotics of random sum and maximum of log-normal risks, in Statist. Probab. Letters
, 87, 167-174.
Dȩbicki Krzysztof, Hashorva Enkelejd, Ji Lanpeng (2014), Tail asymptotics of supremum of certain Gaussian processes over threshold dependent random intervals, in Extremes
, 17(3), 411-429.
Hashorva Enkelejd, Tan Zhongquan (2013), Large deviations of Shepp statistics for fractional Brownian motion, in Statistics & Probability Letters
, 83(10), 2242-2247.
Hashorva Enkelejd (2013), Aggregation of parametrised log-elliptical risks, in Journal of Mathematical Analysis and Applications
, 400(1), 187-199.
Hashorva Enkelejd, Li Jinzhu (2013), ECOMOR and LCR reinsurance with gamma-like claims, in Insurance: Mathematics and Economics
, 53(1), 206-215.
Kortschak Dominik, Hashorva Enkelejd (2013), Efficient simulation of tail probabilities for sums of log-elliptical risks, in Journal of Computational and Applied Mathematics
, 247(1), 53-67.
Tan Zhongquan, Hashorva Enkelejd (2013), Exact asymptotics and limit theorems for supremum of stationary chi-processes over a random interval., in Stoch. Processes Applications
, 123(8), 2983-2998.
Tan Zhongquan, Hashorva Enkelejd (2013), Exact tail asymptotics of the supremum of strongly dependent Gaussian processes over a random interval, in Lithuanian Mathematical Journal
, 53(1), 91-102.
Tan Zhongquan, Hashorva Enkelejd (2013), Limit theorems for extremes of strongly dependent cyclo-stationary chi-processes, in Extremes
, 16(2), 241-254.
Korshunov D.A., Piterbarg V.I., Hashorva E. (2013), On Extremal Behavior of Gaussian Chaos, in Doklady Mathematics
, 88(2), 566-568.
Hashorva Enkelejd, Peng Zuoxiang, Weng Zhichao (2013), On Piterbarg theorem for the maxima of stationary Gaussian sequences, in Lithuanian Math Journal
, 53(3), 280-292.
Tan Zhongquan, Hashorva Enkelejd (2013), On Piterbarg's max-discretisation theorem for multivariate stationary Gaussian processes, in Journal of Mathematical Analysis and Applications
, 409(1), 299-314.
Hashorva Enkelejd, Ji Lanpeng, Piterbarg I Vladimir (2013), On the supremum of gamma-reflected processes with fractional Brownian motion as input, in Stochastic Processes and their Applications
, 123(11), 4111-4127.
Tan Zhongquan, Hashorva Enkelejd, Peng Zuoxiang (2012), Asymptotics of maxima of strongly dependent Gaussian processes, in J. Appl. Probab.
, 49(4), 1106-1118.
Kume Alfred, Hashorva Enkelejd (2012), Calculation of Bayes premium for conditionally elliptical risks, in Insurance: Mathematics and Economics
, 51, 632-635.
The classical Central Limit Theorem and its ramifications show that the Gaussian model is a natural and correct paradigm for building an approximate solution to many otherwise unsolvable problems encountered in various research fields. Indeed, the range of applications of Gaussian processes and related random fields encompasses almost any field of theoretical and applied research. Some extraordinary examplesinclude variations of Brownian motion as the unique solution to problems from theoretical physics, biology, mathematical statistics, risk theory, stochastic finance, telecommunication, just to name a few. While the theory of Gaussian processes and random fields is well-developed and mature, the range of applications of Gaussian random fields is constantly growing. Recently, applications inbrain mapping, cosmology, and quantum chaos have been added to its palmares. Due to the presence of measurement errors, missing observations or random inflations, in some cases the Gaussian framework appears as not tenable. This project advocates that by extending the models to vector-valued chi-processes, vector-valued conditional Gaussian processes and random fields, the Gaussian framework proves to be very reliable.Essentially, numerous applications are intrinsically connected to the study of extremes of Gaussian processes and their related random fields. A natural extreme-value problem in this context is the determination of the exact tail asymptotic behaviour of the maxima of Gaussian processes over some given sets, the hardest and oldest problem in the study of random processes. Besides the tail asymptotics of the maximum, the derivation of limit theorems regarding the maxima of Gaussian processes is both of theoretical and applied interest.This project aims at studying extremes of such large classes of vector-valued Gaussian processes, chi-processes, and conditional Gaussian processes over continuous, discrete and random sets.The principal theoretical findings envisaged by this study shall include both exact tail asymptotic results and limit theorems for the maxima of the mentioned Gaussian and related processes. Since real data are only possible to be observed on a certain discrete grid of time-points,it is planed to investigate the joint asymptotic behaviour of maximum over continuous time intervals with maxima over discrete grids, for several classes of Gaussian processes and chi-processes.Motivated by various applications in risk theory, queueing theory, and hydrodynamics this project is also concerned with the study of the maximum of Gaussian processes and chi-processes over random time intervals. In addition to numerous theoretical results and their interpretation, this project shall develop novel methodologies and techniques. Furthermore, the derivation of some key asymptotical results for the extremes of several Gaussian fields will open the way for novel statistical applications, whereas by focusing on both Gaussian perturbed risk processes and generalsations of the storage processes, additional applications concerned with the risk analysis, simulation of rare-events and the analysis of overflows in hydrodynamics will be promoted.