On Some Limit Theorems Similar to the Arc-Sin Law (1965)

Previous article Next article On Some Limit Theorems Similar to the Arc-Sin LawL. BreimanL. Breimanhttps://doi.org/10.1137/1110037PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] D. A. Darling, The influence of the maximum term in the addition of independent random variables, Trans. Amer. Math. Soc., 73 (1952), 95–107 MR0048726 0047.37502 CrossrefGoogle Scholar[2] A. A. Bobrov, Growth of the maximum term in the sum of independent random variables, Mat. Sb. of Kiev Univ., 5 (1954), 15–38, (In Russian.) Google Scholar[3] D. Z. Arov and , A. A. Bobrov, The extreme terms of a sample and their role in the sum of the independent variables, Theor. Prob. Applications, 85 (1960), 377–396, (English translation.) 10.1137/1105038 0098.11202 LinkGoogle Scholar[4] B. V. Gnedenko and , A. N. Kolmogorov, Limit distributions for sums of independent random variables, Addison-Wesley Publishing Company, Inc., Cambridge, Mass., 1954ix+264 MR0062975 0056.36001 Google Scholar[5] Michel Loève, Probability theory, Third edition, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1963xvi+685 MR0203748 0108.14202 Google Scholar[6] L. Takacs, On a sojourn time problem, Theor. Prob. Applications, 3 (1958), 57–65, (English translation.) LinkGoogle Scholar[7] D. V. Widder, The Laplace Transform, Princeton Univ. Press, Princeton, N. J., 1946 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Tail probabilities of random linear functions of regularly varying random vectors26 May 2022 | Extremes, Vol. 25, No. 4 Cross Ref Modelling extremes of spatial aggregates of precipitation using conditional methodsThe Annals of Applied Statistics, Vol. 16, No. 4 Cross Ref On the tail behaviour of aggregated random variablesJournal of Multivariate Analysis, Vol. 192 Cross Ref Revisiting the Product of Random Variables15 October 2022 | Journal of Mathematical Sciences, Vol. 267, No. 2 Cross Ref Asymptotic ruin probabilities for a dependent renewal risk model with general investment returns and CMC simulations1 October 2022 | Japan Journal of Industrial and Applied Mathematics, Vol. 2 Cross Ref A flexible Bayesian hierarchical modeling framework for spatially dependent peaks-over-threshold dataSpatial Statistics, Vol. 51 Cross Ref Asymptotic dependence of in- and out-degrees in a preferential attachment model with reciprocity30 April 2022 | Extremes, Vol. 25, No. 3 Cross Ref Uniform asymptotics for ruin probabilities of a delayed renewal risk model with one-sided linear dependence and stochastic returns5 August 2022 | Communications in Statistics - Theory and Methods, Vol. 51 Cross Ref Continuous scaled phase-type distributions5 July 2022 | Stochastic Models, Vol. 23 Cross Ref Asymptotic estimates for finite-time ruin probability in a discrete-time risk model with dependence structures and CMC simulations5 August 2020 | Communications in Statistics - Theory and Methods, Vol. 51, No. 11 Cross Ref Portmanteau-type test for unit root with heavy-tailed noiseJournal of Statistical Planning and Inference, Vol. 218 Cross Ref Distribution tails of a history-dependent random linear recursion11 January 2022 | Stochastic Models, Vol. 38, No. 2 Cross Ref An asymptotic study of systemic expected shortfall and marginal expected shortfallInsurance: Mathematics and Economics Cross Ref TAIL DEPENDENCE OF OLS2 July 2021 | Econometric Theory, Vol. 38, No. 2 Cross Ref CHARACTERIZATION OF THE TAIL BEHAVIOR OF A CLASS OF BEKK PROCESSES: A STOCHASTIC RECURRENCE EQUATION APPROACH4 February 2021 | Econometric Theory, Vol. 38, No. 1 Cross Ref Ruin probability of a continuous-time model with dependence between insurance and financial risks caused by systematic factorsApplied Mathematics and Computation, Vol. 413 Cross Ref Phase transition for extremes of a stochastic model with long-range dependence and multiplicative noiseStochastic Processes and their Applications, Vol. 143 Cross Ref Uniform asymptotics for ruin probabilities of a time-dependent renewal risk model with dependence structures and stochastic returns8 November 2021 | Communications in Statistics - Theory and Methods Cross Ref Large portfolio losses in a turbulent marketEuropean Journal of Operational Research, Vol. 292, No. 2 Cross Ref Spatial hierarchical modeling of threshold exceedances using rate mixtures14 December 2020 | Environmetrics, Vol. 32, No. 3 Cross Ref ASYMPTOTICS FOR SYSTEMIC RISK WITH DEPENDENT HEAVY-TAILED LOSSES29 April 2021 | ASTIN Bulletin, Vol. 71 Cross Ref Precise large deviations for dependent subexponential variablesBernoulli, Vol. 27, No. 2 Cross Ref Hierarchical Transformed Scale Mixtures for Flexible Modeling of Spatial Extremes on Datasets with Many Locations7 December 2020 | Journal of the American Statistical Association Cross Ref Homogeneous mappings of regularly varying vectorsThe Annals of Applied Probability, Vol. 30, No. 6 Cross Ref On the emergence of a power law in the distribution of COVID-19 casesPhysica D: Nonlinear Phenomena, Vol. 412 Cross Ref Extremal dependence of random scale constructions12 July 2019 | Extremes, Vol. 22, No. 4 Cross Ref Simple models for multivariate regular variation and the Hüsler–Reiß Pareto distributionJournal of Multivariate Analysis, Vol. 173 Cross Ref On posterior consistency of tail index for Bayesian kernel mixture modelsBernoulli, Vol. 25, No. 3 Cross Ref Bivariate regular variation among randomly weighted sums in general insurance9 March 2019 | European Actuarial Journal, Vol. 9, No. 1 Cross Ref Interplay of insurance and financial risks in a stochastic environment19 February 2019 | Scandinavian Actuarial Journal, Vol. 2019, No. 5 Cross Ref Tail asymptotic for discounted aggregate claims with one-sided linear dependence and general investment return6 December 2018 | Science China Mathematics, Vol. 62, No. 4 Cross Ref References25 March 2019 Cross Ref On a Lower Asymptotic Bound of the Overflow Probability in a Fluid Queue with a Heterogeneous Fractional Input9 February 2019 | Journal of Mathematical Sciences, Vol. 237, No. 5 Cross Ref Extensions of Breiman's Theorem of Product of Dependent Random Variables with Applications to Ruin Theory21 June 2018 | Communications in Mathematics and Statistics, Vol. 7, No. 1 Cross Ref Tail asymptotic of discounted aggregate claims with compound dependence under risky investment10 January 2018 | Communications in Statistics - Theory and Methods, Vol. 48, No. 4 Cross Ref Fundamental Limits of Ultra-dense Networks1 February 2019 Cross Ref The tail empirical process for long memory stochastic volatility models with leverageElectronic Journal of Statistics, Vol. 13, No. 2 Cross Ref When Simplicity Offers a Benefit, Not a Cost: Closed-Form Estimation of the GARCH(1,1) Model that Enhances the Efficiency of Quasi-Maximum Likelihood: Supplemental AppendixSSRN Electronic Journal Cross Ref Randomly weighted sums under a wide type of dependence structure with application to conditional tail expectation8 November 2017 | Communications in Statistics - Theory and Methods, Vol. 47, No. 20 Cross Ref The finite-time ruin probability of a discrete-time risk model with GARCH discounted factors and dependent risks31 October 2017 | Communications in Statistics - Theory and Methods, Vol. 47, No. 17 Cross Ref The joint distribution of the sum and maximum of dependent Pareto risksJournal of Multivariate Analysis, Vol. 167 Cross Ref Asymptotic tail behaviour of phase-type scale mixture distributions29 August 2017 | Annals of Actuarial Science, Vol. 12, No. 2 Cross Ref On perpetuities with gamma-like tails26 July 2018 | Journal of Applied Probability, Vol. 55, No. 2 Cross Ref The eigenvalues of the sample covariance matrix of a multivariate heavy-tailed stochastic volatility modelBernoulli, Vol. 24, No. 2 Cross Ref Uniform asymptotics for ruin probabilities in a dependent renewal risk model with stochastic return on investments28 August 2017 | Stochastics, Vol. 90, No. 3 Cross Ref On the joint tail behavior of randomly weighted sums of heavy-tailed random variablesJournal of Multivariate Analysis, Vol. 164 Cross Ref Joint exceedances of random productsAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques, Vol. 54, No. 1 Cross Ref A note on stable limit theory for the OLSE with non usual rates and the heteroskedasticity robust Wald test8 September 2017 | Communications in Statistics - Theory and Methods, Vol. 47, No. 1 Cross Ref The GJR GARCH(1,1) Process As Regularly Varying: Implications for Efficient Model Estimation and Risk MeasurementSSRN Electronic Journal Cross Ref Boolean convolutions and regular variationLatin American Journal of Probability and Mathematical Statistics, Vol. 15, No. 2 Cross Ref A general approach to full-range tail dependence copulasInsurance: Mathematics and Economics, Vol. 77 Cross Ref References1 September 2017 Cross Ref Extremal attractors of Liouville copulasJournal of Multivariate Analysis, Vol. 160 Cross Ref Performance Limits of Network DensificationIEEE Journal on Selected Areas in Communications, Vol. 35, No. 6 Cross Ref Asymptotic Estimates for the One-Year Ruin Probability under Risky Investments6 May 2017 | Risks, Vol. 5, No. 2 Cross Ref Multivariate Hill Estimators29 October 2015 | International Statistical Review, Vol. 85, No. 1 Cross Ref On relative stability and weighted laws of large numbers28 September 2016 | Extremes, Vol. 20, No. 1 Cross Ref A revisit to ruin probabilities in the presence of heavy-tailed insurance and financial risksInsurance: Mathematics and Economics, Vol. 73 Cross Ref Sequential monitoring of the tail behavior of dependent dataJournal of Statistical Planning and Inference, Vol. 182 Cross Ref Asymptotics for ruin probabilities of a non-standard renewal risk model with dependence structures and exponential Lévy process investment returnsJournal of Industrial & Management Optimization, Vol. 13, No. 1 Cross Ref Infinite-time ruin probability of a renewal risk model with exponential Levy process investment and dependent claims and inter-arrival timesJournal of Industrial & Management Optimization, Vol. 13, No. 2 Cross Ref Assessing component reliability using lifetime data from systems19 May 2016 | Journal of Statistical Computation and Simulation, Vol. 86, No. 18 Cross Ref Bounds for randomly shared risk of heavy-tailed loss factors2 April 2016 | Extremes, Vol. 19, No. 4 Cross Ref The ruin probabilities of a discrete-time risk model with dependent insurance and financial risksJournal of Mathematical Analysis and Applications, Vol. 444, No. 1 Cross Ref A Note on Upper Tail Behavior of Liouville Copulas8 November 2016 | Risks, Vol. 4, No. 4 Cross Ref Uniform asymptotics for a multi-dimensional time-dependent risk model with multivariate regularly varying claims and stochastic returnInsurance: Mathematics and Economics, Vol. 71 Cross Ref Extremes for coherent risk measuresInsurance: Mathematics and Economics, Vol. 71 Cross Ref Ruin probabilities under Sarmanov dependence structureStatistics & Probability Letters, Vol. 117 Cross Ref Risk in a Large Claims Insurance Market with Bipartite Graph StructureOperations Research, Vol. 64, No. 5 Cross Ref A stochastic volatility model with flexible extremal dependence structureBernoulli, Vol. 22, No. 3 Cross Ref The extremogram and the cross-extremogram for a bivariate GARCH(1, 1) process25 July 2016 | Advances in Applied Probability, Vol. 48, No. A Cross Ref Poisson Process Driven Stochastic Differential Equations for bivariate heavy tailed distributions Cross Ref Coverage and capacity scaling laws in downlink ultra-dense cellular networks Cross Ref Asymptotic behavior of the generalized St. Petersburg sum conditioned on its maximumBernoulli, Vol. 22, No. 2 Cross Ref Functional weak convergence of partial maxima processes19 December 2015 | Extremes, Vol. 19, No. 1 Cross Ref Asymptotic behaviour of multivariate default probabilities and default correlations under stress24 March 2016 | Journal of Applied Probability, Vol. 53, No. 1 Cross Ref Asymptotic ruin probabilities for a discrete-time risk model with dependent insurance and financial risks5 February 2014 | Scandinavian Actuarial Journal, Vol. 2016, No. 1 Cross Ref Perturbed Random Walks11 December 2016 Cross Ref GEL estimation for heavy-tailed GARCH models with robust empirical likelihood inferenceJournal of Econometrics, Vol. 190, No. 1 Cross Ref Extremes for Coherent Risk MeasuresSSRN Electronic Journal Cross Ref Simple Estimators for ARCH Models: Supplemental AppendixSSRN Electronic Journal Cross Ref Interplay of Insurance and Financial Risks with Bivariate Regular Variation7 January 2016 Cross Ref Models with Hidden Regular Variation: Generation and DetectionStochastic Systems, Vol. 5, No. 2 Cross Ref Asymptotics for ruin probabilities in a discrete-time risk model with dependent financial and insurance risks15 January 2014 | Scandinavian Actuarial Journal, Vol. 2015, No. 8 Cross Ref Calculation of ruin probabilities for a dense class of heavy tailed distributions15 January 2014 | Scandinavian Actuarial Journal, Vol. 2015, No. 7 Cross Ref Limit Theory for the QMLE of the GQARCH (1,1) Model1 April 2015 | Communications in Statistics - Theory and Methods, Vol. 44, No. 17 Cross Ref Asymptotic expansion of Gaussian chaos via probabilistic approach10 March 2015 | Extremes, Vol. 18, No. 3 Cross Ref Aggregation of randomly weighted large risks3 August 2015 | IMA Journal of Management Mathematics, Vol. 2 Cross Ref The integrated periodogram of a dependent extremal event sequenceStochastic Processes and their Applications, Vol. 125, No. 8 Cross Ref ASYMPTOTIC INFERENCE FOR AR MODELS WITH HEAVY-TAILED G-GARCH NOISES3 November 2014 | Econometric Theory, Vol. 31, No. 4 Cross Ref Robust estimation and inference for heavy tailed GARCHBernoulli, Vol. 21, No. 3 Cross Ref Interplay of insurance and financial risks in a discrete-time model with strongly regular variationBernoulli, Vol. 21, No. 3 Cross Ref Asymptotic ruin probabilities for a bidimensional renewal risk model with constant interest rate and dependent claimsJournal of Mathematical Analysis and Applications, Vol. 426, No. 1 Cross Ref Ruin with insurance and financial risks following the least risky FGM dependence structureInsurance: Mathematics and Economics, Vol. 62 Cross Ref CORRELATION UNDER STRESS IN NORMAL VARIANCE MIXTURE MODELS18 February 2013 | Mathematical Finance, Vol. 25, No. 2 Cross Ref Joint extremal behavior of hidden and observable time series with applications to GARCH processes9 October 2014 | Extremes, Vol. 18, No. 1 Cross Ref On functional limits of short- and long-memory linear processes with GARCH(1,1) noisesStochastic Processes and their Applications, Vol. 125, No. 2 Cross Ref Robust score and portmanteau tests of volatility spilloverJournal of Econometrics, Vol. 184, No. 1 Cross Ref The finite-time ruin probability with heavy-tailed and dependent insurance and financial risksInsurance: Mathematics and Economics, Vol. 59 Cross Ref ASYMPTOTICS FOR A RISK WITH THE June 2014 | Probability in the and Sciences, Vol. No. 4 Cross Ref Randomly weighted sums of subexponential random with application to May 2014 | Extremes, Vol. No. 3 Cross Ref Regular of of Processes with Random July 2014 | Stochastic Models, Vol. 30, No. 3 Cross Ref The index of regularly varying with applications to limit theory for functions of multivariate June 2013 | Probability Theory and Vol. No. Cross Ref Ruin probabilities with insurance and financial risks FGM dependence January 2014 | Science China Mathematics, Vol. No. 5 Cross Ref tail asymptotics of risksInsurance: Mathematics and Economics, Vol. Cross Ref A of extreme Vol. 20, No. 2 Cross Ref On for Some Processes with Dependent February 2016 | Journal of Applied Probability, Vol. 51, No. Cross Ref On for Some Processes with Dependent January 2018 | Journal of Applied Probability, Vol. 51, No. 1 Cross Ref The of of from time series February 2013 | Extremes, Vol. 16, No. 4 Cross Ref Modeling and applications in March | and Applications, Vol. No. 3 Cross Ref Fractional of to Stochastic March 2016 | Journal of Applied Probability, Vol. No. Cross Ref Fractional of to Stochastic January 2018 | Journal of Applied Probability, Vol. No. 4 Cross Ref GARCH models of Econometrics, Vol. No. 1 Cross Ref Stochastic volatility models with extremal Vol. 19, No. Cross Ref for stochastic with heavy-tailed on Modeling and Simulation, Vol. No. 4 Cross Ref Limit theory of of long-memory linear processes with heavy-tailed GARCH of Multivariate Analysis, Vol. Cross Ref of the of dependent random & Probability Letters, Vol. No. Cross Ref Precise large deviations for dependent regularly varying July | Probability Theory and Vol. No. Cross Ref OF INFERENCE THE FOR WITH January 2013 | Econometric Theory, Vol. No. 4 Cross Ref distributions for random in a random de l'Institut Henri Poincaré, Probabilités et Statistiques, Vol. No. 3 Cross Ref and maxima of and Vol. 19, No. 3 Cross Ref of the tail probability of the of dependent extremal random and Mathematics and Economics, Vol. 53, No. 1 Cross Ref Estimation of conditional distributions for the heavy tailed long memory stochastic volatility October | Extremes, Vol. 16, No. 2 Cross Ref Tail behavior of the of dependent random with applications to risk June | Extremes, Vol. 16, No. 1 Cross Ref Extremes and of multivariate risksInsurance: Mathematics and Economics, Vol. No. 2 Cross Ref and Ruin with Stochastic Processes and Bivariate Upper Tail and January 2016 | Advances in Applied Probability, Vol. No. Cross Ref Asymptotics of Fluid with Lévy March 2016 | Journal of Applied Probability, Vol. No. Cross Ref and Ruin with Stochastic Processes and Bivariate Upper Tail and January 2016 | Advances in Applied Probability, Vol. No. 1 Cross Ref Asymptotics of Fluid with Lévy January 2018 | Journal of Applied Probability, Vol. No. 1 Cross Ref tails of of Econometrics, Vol. No. 2 Cross Ref On consistency of the least in linear models with Journal of Statistics, Vol. 7, No. Cross Ref A Multivariate Hill Electronic Journal Cross Ref Robust Estimation and for Electronic Journal Cross Ref The extremal index for GARCH(1, 1) March | Extremes, Vol. 15, No. 4 Cross Ref Asymptotic Ruin for a Bivariate Risk Model with Claims and Risky March 2016 | Journal of Applied Probability, Vol. No. Cross Ref Asymptotic Ruin for a Bivariate Risk Model with Claims and Risky January 2018 | Journal of Applied Probability, Vol. No. 4 Cross Ref Tail and asymptotic of risk measuresInsurance: Mathematics and Economics, Vol. 51, No. 2 Cross Ref Tail Behavior of Randomly January 2016 | Advances in Applied Probability, Vol. 44, No. Cross Ref of GARCH(1, 1) process with heavy tailed Cross Ref Tail Behavior of Randomly January 2016 | Advances in Applied Probability, Vol. 44, No. 3 Cross Ref stability in random Processes and their Applications, Vol. No. 8 Cross Ref On the regular variation of of random April | Extremes, Vol. 15, No. 2 Cross Ref Asymptotics in a time-dependent renewal risk model with stochastic of Mathematical Analysis and Applications, Vol. No. 2 Cross Ref Tail index estimation in the presence of long-memory Statistics & Analysis, Vol. No. 2 Cross Ref The Joint Distribution of the and the of Random in Statistics - Theory and Methods, Vol. No. 3 Cross Ref deviations for a risk model on the & Probability Letters, Vol. No. 1 Cross Ref Limit theory for a general class of GARCH models with July | Journal of Analysis, Vol. No. 1 Cross Ref Tail for Regularly in Vol. Cross Ref The asymptotic distribution of randomly weighted sums and Journal of Probability, Vol. No. Cross Ref Tail Asymptotics of the of Electronic Journal Cross Ref The tail probability of the of dependent random from of & Probability Letters, Vol. No. Cross Ref The Ruin Probability with Dependent Insurance and Financial July 2016 | Journal of Applied Probability, Vol. 48, No. Cross Ref The Ruin Probability with Dependent Insurance and Financial July 2016 | Journal of Applied Probability, Vol. 48, No. 4 Cross Ref in and application to ruin Mathematics and Economics, Vol. No. 3 Cross Ref regular variation and conditional tail of risksInsurance: Mathematics and Economics, Vol. No. 3 Cross Ref limits for sums of dependent random March | Probability Theory and Vol. No. Cross Ref The of dependent random with regularly varying varying & Probability Letters, Vol. No. 8 Cross Ref Uniform estimates for ruin probabilities in the renewal risk model with independent claims and of Industrial and Management Optimization, Vol. 7, No. 4 Cross Ref Extremal memory of stochastic volatility with application to tail inferenceJournal of Statistical Planning and Inference, Vol. No. 2 Cross Ref for of Stochastic Equations and for February Cross Ref The of the to and to September Cross Ref The tail empirical process for long memory stochastic volatility Processes and their Applications, Vol. No. 1 Cross Ref in and on Theory, Vol. No. 1 Cross Ref GEL Estimation for GARCH with Robust Electronic Journal Cross Ref Asymptotics of random Mathematics and Economics, Vol. 47, No. 3 Cross Ref Tail asymptotics under random of Mathematical Analysis and Applications, Vol. No. 2 Cross Ref memory in and volatility of of Statistical Planning and Inference, Vol. No. Cross Ref On Perturbed Random July 2016 | Journal of Applied Probability, Vol. 47, No. Cross Ref On Perturbed Random July 2016 | Journal of Applied Probability, Vol. 47, No. 4 Cross Ref THE OF May | Journal of the Mathematical Vol. No. 2 Cross Ref of of stable random July 2016 | Advances in Applied Probability, Vol. No. Cross Ref of of stable random July 2016 | Advances in Applied Probability, Vol. No. 2 Cross Ref May Cross Ref Uniform tail asymptotics for the stochastic of aggregate claims in the renewal risk Mathematics and Economics, Vol. No. 2 Cross Ref dependence in time series April | Extremes, Vol. 13, No. 1 Cross Ref Limit for Bivariate with Models, Vol. No. 1 Cross Ref Asymptotic for sample functions and extremes of integrated generalized Vol. 16, No. 1 Cross Ref Estimation for a linear model with Journal of Statistics, Vol. 4, No. Cross Ref in Electronic Journal Cross Ref of distribution tails and estimation of tail in random March | Extremes, Vol. 12, No. 4 Cross Ref Uniform for of Randomly with Applications to Ruin July | and in Applied Probability, Vol. No. 4 Cross Ref Randomly of Random Variables with Cross Ref The A for extreme Vol. 15, No. 4 Cross Ref Random and ruin in a stochastic Annals of Applied Probability, Vol. 19, No. 4 Cross Ref Extremes of threshold July 2016 | Advances in Applied Probability, Vol. No. 2 Cross Ref Regularly varying multivariate time Processes and their Applications, Vol. No. 4 Cross Ref for with Cross Ref for regular variation of linear a for and of stable Annals of Applied Probability, Vol. 19, No. 1 Cross Ref of Stochastic February Cross Ref Extremes of February Cross Ref Theory for GARCH February Cross Ref Estimation of the with of February | and Vol. No. 1 Cross Ref to Electronic Journal Cross Ref Tail probabilities for series of regularly varying random Vol. No. 3 Cross Ref Tail behaviour and extremes of & Mathematics with Applications, Vol. 55, No. Cross Ref theory for processes with heavy-tailed Processes and their Applications, Vol. No. 4 Cross Ref Tail behavior of random and stochastic Processes and their Applications, Vol. No. 3 Cross Ref The influence of dependence on data July 2016 | Advances in Applied Probability, Vol. No. Cross Ref The influence of dependence on data July 2016 | Advances in Applied Probability, Vol. No. 1 Cross Ref Asymptotic behavior of the tail probability for Statistical and its Applications, Vol. No. Cross Ref Asymptotics for long dependent of Econometrics, Vol. No. 2 Cross Ref On a Theorem of and a of Random July 2016 | Journal of Applied Probability, Vol. 44, No. Cross Ref On a Theorem of and a of Random July 2016 | Journal of Applied Probability, Vol. 44, No. 4 Cross Ref The of the extreme to the sum in a random October | Extremes, Vol. No. 4 Cross Ref On the extremes of a class of processes with heavy tailed Theory, Methods & Applications, Vol. No. 7 Cross Ref A of the and Vol. No. Cross Ref Asymptotics for with Applications to March | and in Applied Probability, Vol. 9, No. 2 Cross Ref A May | Systems, Vol. No. 1 Cross Ref in Some capacity scaling laws Cross Ref Tail behavior of conditional sojourn in December | Systems, Vol. 55, No. 2 Cross Ref On the of the maximum of the of random of Statistical Planning and Inference, Vol. No. 3 Cross Ref Extremal behavior of stochastic by regularly varying Lévy Annals of Probability, Vol. 35, No. 1 Cross Ref of November | Journal of Probability, Vol. 19, No. 4 Cross Ref THE TAIL OF A OF GARCH August | Econometric Theory, Vol. 22, No. Cross Ref On the regular variation of random & Probability Letters, Vol. No. Cross Ref On the tail of threshold GARCH(1,1) & Probability Letters, Vol. No. Cross Ref dependence of multivariate Actuarial Journal, Vol. No. 4 Cross Ref Tail of Randomly of Random Variables with September | Stochastic Models, Vol. 22, No. 2 Cross Ref On a GARCH of Analysis, Vol. 27, No. 4 Cross Ref time asymptotics in Systems, Vol. 53, No. Cross Ref models of July 2016 | Advances in Applied Probability, Vol. 38, No. Cross Ref On a process with heavy-tailed renewal and heavy-tailed July 2016 | Journal of Applied Probability, Vol. No. Cross Ref models of July 2016 | Advances in Applied Probability, Vol. 38, No. 2 Cross Ref On a process with heavy-tailed renewal and heavy-tailed July 2016 | Journal of Applied Probability, Vol. No. 2 Cross Ref and Market Journal of Economics, Vol. No. 2 Cross Ref Limit Theorems for with Random and July 2016 | Journal of Applied Probability, Vol. No. 1 Cross Ref limits of with application to the estimation of GARCH Annals of Statistics, Vol. No. 1 Cross Ref Regularly varying de l'Institut Vol. No. Cross Ref Extremal stochastic a between processes and June | Extremes, Vol. No. 4 Cross Ref Extremes of regularly varying July 2016 | Advances in Applied Probability, Vol. No. Cross Ref Extremes of regularly varying July 2016 | Advances in Applied Probability, Vol. No. 4 Cross Ref and stable limit of Econometrics, Vol. No. Cross Ref The Tail Probability of of in Actuarial Journal, Vol. No. 6 Cross Ref Some asymptotic for sums of dependent random variables, with Mathematics and Economics, Vol. No. 2 Cross Ref Large deviations and ruin probabilities for to stochastic with heavy-tailed Annals of Probability, Vol. No. 5 Cross Ref Extremes of and random Mathematics and Economics, Vol. No. 3 Cross Ref When a Randomly in Communications in Probability, Vol. No. Cross Ref The Extremal and Asymptotic September | Stochastic Models, Vol. 20, No. 2 Cross Ref Limit for processes with renewal Annals of Applied Probability, Vol. No. 4 Cross Ref Joint exceedances of the ARCH July 2016 | Journal of Applied Probability, Vol. No. Cross Ref Joint exceedances of the ARCH July 2016 | Journal of Applied Probability, Vol. No. 3 Cross Ref The of a Gaussian process a random & Probability Letters, Vol. No. 3 Cross Ref and July 2016 | Journal of Applied Probability, Vol. No. Cross Ref and July 2016 | Journal of Applied Probability, Vol. No. 2 Cross Ref and of Hidden Regular January | Extremes, Vol. 7, No. 1 Cross Ref and for processes the and the Vol. No. 1 Cross Ref Precise estimates for the ruin probability in in a discrete-time model with heavy-tailed insurance and financial Processes and their Applications, Vol. No. 2 Cross Ref Advances in Applied Probability Applied July 2016 | Advances in Applied Probability, Vol. 35, No. 4 Cross Ref Random and long July 2016 | Advances in Applied Probability, Vol. 35, No. Cross Ref Random and long July 2016 | Advances in Applied Probability, Vol. 35, No. 3 Cross Ref A Theory of Large in Market Electronic Journal Cross Ref Asymptotic and a July 2016 | Journal of Applied Probability, Vol. No. Cross Ref Asymptotic and a July 2016 | Journal of Applied Probability, Vol. No. 4 Cross Ref of tails by Statistical and its Applications, Vol. No. Cross Ref Regular variation of GARCH Processes and their Applications, Vol. No. 1 Cross Ref of and of de l'Institut Vol. No. 85 Cross Ref to Statistical and its Applications, Vol. No. Cross Ref process convergence of stochastic volatility processes with application to sample July 2016 | Journal of Applied Probability, Vol. 38, No. A Cross Ref Limit theory for the sample and extremes of a GARCH (1,1) Annals of Statistics, Vol. No. 5 Cross Ref behavior for the heavy tailed general in Stochastic Models, Vol. 16, No. 2 Cross Ref On and Electronic Journal Cross Ref The sample of a Processes and their Applications, Vol. No. 1 Cross Ref The sample of heavy-tailed processes with applications to Annals of Statistics, Vol. No. 5 Cross Ref estimation for with Annals of Applied Probability, Vol. No. 4 Cross Ref Limit theory for processes with heavy-tailed Annals of Applied Probability, Vol. No. 4 Cross Ref between tail of lifetime distributions and of of the of Statistical Mathematics, Vol. 48, No. 2 Cross Ref Limit distributions for linear time series Processes and their Applications, Vol. 51, No. 1 Cross Ref of the of independent random Processes and their Applications, Vol. No. 1 Cross Ref Estimation for processes with in Stochastic Models, Vol. No. 3 Cross Ref a and February | Econometric Theory, Vol. No. 1 Cross Ref for least with dataJournal of Statistical Planning and Inference, Vol. No. 2 Cross Ref Estimation for processes with Processes and their Applications, Vol. 31, No. 2 Cross Ref Joint stable of sums of of Multivariate Analysis, Vol. 25, No. 2 Cross Ref tails and of Theory and Vol. No. 4 Cross Ref regular variation and weak July 2016 | Advances in Applied Probability, Vol. 18, No. Cross Ref regular variation and weak July 2016 | Advances in Applied Probability, Vol. 18, No. 1 Cross Ref limit theory for the sample of Processes and their Applications, Vol. 20, No. 2 Cross Ref in Insurance Mathematics Cross Ref On and of subexponential and April | Journal of the Mathematical A. Mathematics and Statistics, Vol. No. 2 Cross Ref Extremal behavior of stochastic volatility models Cross Ref of the by of Some Vol. 7, No. Cross Ref of Probability & Applications October July for Industrial and Applied & for Industrial and Applied Mathematics