On Some Limit Theorems Similar to the Arc-Sin Law

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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 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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 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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 DISCRETE-TIME RISK MODEL WITH THE EMPHASIS ON FINANCIAL RISK27 June 2014 | Probability in the Engineering and Informational Sciences, Vol. 28, No. 4 Cross Ref Randomly weighted sums of subexponential random variables with application to capital allocation4 May 2014 | Extremes, Vol. 17, No. 3 Cross Ref Regular Variation of Infinite Series of Processes with Random Coefficients28 July 2014 | Stochastic Models, Vol. 30, No. 3 Cross Ref The cluster index of regularly varying sequences with applications to limit theory for functions of multivariate Markov chains8 June 2013 | Probability Theory and Related Fields, Vol. 159, No. 1-2 Cross Ref Ruin probabilities with insurance and financial risks having an FGM dependence structure24 January 2014 | Science China Mathematics, Vol. 57, No. 5 Cross Ref Second-order tail asymptotics of deflated risksInsurance: Mathematics and Economics, Vol. 56 Cross Ref A Fourier analysis of extreme eventsBernoulli, Vol. 20, No. 2 Cross Ref On Exceedance Times for Some Processes with Dependent Increments19 February 2016 | Journal of Applied Probability, Vol. 51, No. 01 Cross Ref On Exceedance Times for Some Processes with Dependent Increments30 January 2018 | Journal of Applied Probability, Vol. 51, No. 1 Cross Ref The convex hull of consecutive pairs of observations from some time series models7 February 2013 | Extremes, Vol. 16, No. 4 Cross Ref Modeling and evaluating IPTV applications in WiMAX networks18 March 2012 | Multimedia Tools and Applications, Vol. 67, No. 3 Cross Ref Fractional Moments of Solutions to Stochastic Recurrence Equations1 March 2016 | Journal of Applied Probability, Vol. 50, No. 04 Cross Ref Fractional Moments of Solutions to Stochastic Recurrence Equations30 January 2018 | Journal of Applied Probability, Vol. 50, No. 4 Cross Ref GARCH models without positivity constraints: Exponential or log GARCH?Journal of Econometrics, Vol. 177, No. 1 Cross Ref Stochastic volatility models with possible extremal clusteringBernoulli, Vol. 19, No. 5A Cross Ref Rare-event simulation for stochastic recurrence equations with heavy-tailed innovationsACM Transactions on Modeling and Computer Simulation, Vol. 23, No. 4 Cross Ref Limit theory of quadratic forms of long-memory linear processes with heavy-tailed GARCH innovationsJournal of Multivariate Analysis, Vol. 120 Cross Ref Subexponentiality of the product of dependent random variablesStatistics & Probability Letters, Vol. 83, No. 9 Cross Ref Precise large deviations for dependent regularly varying sequences31 July 2012 | Probability Theory and Related Fields, Vol. 156, No. 3-4 Cross Ref ESTIMATION OF AND INFERENCE ABOUT THE EXPECTED SHORTFALL FOR TIME SERIES WITH INFINITE VARIANCE16 January 2013 | Econometric Theory, Vol. 29, No. 4 Cross Ref Weak quenched limiting distributions for transient one-dimensional random walk in a random environmentAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques, Vol. 49, No. 3 Cross Ref Minima and maxima of elliptical arrays and spherical processesBernoulli, Vol. 19, No. 3 Cross Ref Approximations of the tail probability of the product of dependent extremal random variables and applicationsInsurance: Mathematics and Economics, Vol. 53, No. 1 Cross Ref Estimation of limiting conditional distributions for the heavy tailed long memory stochastic volatility process2 October 2012 | Extremes, Vol. 16, No. 2 Cross Ref Tail behavior of the product of two dependent random variables with applications to risk theory22 June 2012 | Extremes, Vol. 16, No. 1 Cross Ref Extremes and products of multivariate AC-product risksInsurance: Mathematics and Economics, Vol. 52, No. 2 Cross Ref Finite- and Infinite-Time Ruin Probabilities with General Stochastic Investment Return Processes and Bivariate Upper Tail Independent and Heavy-Tailed Claims4 January 2016 | Advances in Applied Probability, Vol. 45, No. 01 Cross Ref Asymptotics of Hybrid Fluid Queues with Lévy Input1 March 2016 | Journal of Applied Probability, Vol. 50, No. 01 Cross Ref Finite- and Infinite-Time Ruin Probabilities with General Stochastic Investment Return Processes and Bivariate Upper Tail Independent and Heavy-Tailed Claims4 January 2016 | Advances in Applied Probability, Vol. 45, No. 1 Cross Ref Asymptotics of Hybrid Fluid Queues with Lévy Input30 January 2018 | Journal of Applied Probability, Vol. 50, No. 1 Cross Ref Heavy tails of OLSJournal of Econometrics, Vol. 172, No. 2 Cross Ref On consistency of the least squares estimators in linear errors-in-variables models with infinite variance errorsElectronic Journal of Statistics, Vol. 7, No. none Cross Ref A Multivariate Hill EstimatorSSRN Electronic Journal Cross Ref Robust Estimation and Inference for Heavy Tailed GARCHSSRN Electronic Journal Cross Ref The extremal index for GARCH(1, 1) processes8 March 2012 | Extremes, Vol. 15, No. 4 Cross Ref Asymptotic Ruin Probabilities for a Bivariate Lévy-Driven Risk Model with Heavy-Tailed Claims and Risky Investments1 March 2016 | Journal of Applied Probability, Vol. 49, No. 04 Cross Ref Asymptotic Ruin Probabilities for a Bivariate Lévy-Driven Risk Model with Heavy-Tailed Claims and Risky Investments30 January 2018 | Journal of Applied Probability, Vol. 49, No. 4 Cross Ref Tail comonotonicity: Properties, constructions, and asymptotic additivity of risk measuresInsurance: Mathematics and Economics, Vol. 51, No. 2 Cross Ref Tail Behavior of Randomly Weighted Sums4 January 2016 | Advances in Applied Probability, Vol. 44, No. 03 Cross Ref Parameters estimator of GARCH(1, 1) process with heavy tailed errors Cross Ref Tail Behavior of Randomly Weighted Sums4 January 2016 | Advances in Applied Probability, Vol. 44, No. 3 Cross Ref Relative stability in strictly stationary random sequencesStochastic Processes and their Applications, Vol. 122, No. 8 Cross Ref On the regular variation of ratios of jointly Fréchet random variables7 April 2011 | Extremes, Vol. 15, No. 2 Cross Ref Asymptotics in a time-dependent renewal risk model with stochastic returnJournal of Mathematical Analysis and Applications, Vol. 387, No. 2 Cross Ref Tail index estimation in the presence of long-memory dynamicsComputational Statistics & Data Analysis, Vol. 56, No. 2 Cross Ref The Joint Distribution of the Sum and the Maximum of IID Exponential Random VariablesCommunications in Statistics - Theory and Methods, Vol. 41, No. 3 Cross Ref Moderate deviations for a risk model based on the customer-arrival processStatistics & Probability Letters, Vol. 82, No. 1 Cross Ref Limit theory for a general class of GARCH models with just barely infinite variance27 July 2011 | Journal of Time Series Analysis, Vol. 33, No. 1 Cross Ref Tail Dependence for Regularly Varying Time SeriesMathematical Problems in Engineering, Vol. 2012 Cross Ref The asymptotic distribution of randomly weighted sums and self-normalized sumsElectronic Journal of Probability, Vol. 17, No. none Cross Ref Exact Tail Asymptotics of the Total Loss of Largest Claim Reinsurance TreatiesSSRN Electronic Journal Cross Ref The tail probability of the product of dependent random variables from max-domains of attractionStatistics & Probability Letters, Vol. 81, No. 12 Cross Ref The Finite-Time Ruin Probability with Dependent Insurance and Financial Risks14 July 2016 | Journal of Applied Probability, Vol. 48, No. 04 Cross Ref The Finite-Time Ruin Probability with Dependent Insurance and Financial Risks14 July 2016 | Journal of Applied Probability, Vol. 48, No. 4 Cross Ref Archimedean copulas in finite and infinite dimensions—with application to ruin problemsInsurance: Mathematics and Economics, Vol. 49, No. 3 Cross Ref Second order regular variation and conditional tail expectation of multiple risksInsurance: Mathematics and Economics, Vol. 49, No. 3 Cross Ref Stable limits for sums of dependent infinite variance random variables11 March 2010 | Probability Theory and Related Fields, Vol. 150, No. 3-4 Cross Ref The product of two dependent random variables with regularly varying or rapidly varying tailsStatistics & Probability Letters, Vol. 81, No. 8 Cross Ref Uniform estimates for ruin probabilities in the renewal risk model with upper-tail independent claims and premiumsJournal of Industrial and Management Optimization, Vol. 7, No. 4 Cross Ref Extremal memory of stochastic volatility with an application to tail shape inferenceJournal of Statistical Planning and Inference, Vol. 141, No. 2 Cross Ref Auto-tail Dependence Coefficients for Stationary Solutions of Linear Stochastic Recurrence Equations and for GARCH(1,1)4 February 2011 Cross Ref The Distributions of the Peak to Average and Peak to Sum Ratios Under Exponentiality27 September 2010 Cross Ref The tail empirical process for long memory stochastic volatility sequencesStochastic Processes and their Applications, Vol. 121, No. 1 Cross Ref Rate Scaling Laws in Multicell Networks Under Distributed Power Control and User SchedulingIEEE Transactions on Information Theory, Vol. 57, No. 1 Cross Ref GEL Estimation for Semi-Strong Non-Linear GARCH with Robust Empirical Likelihood InferenceSSRN Electronic Journal Cross Ref Asymptotics of random contractionsInsurance: Mathematics and Economics, Vol. 47, No. 3 Cross Ref Tail asymptotics under beta random scalingJournal of Mathematical Analysis and Applications, Vol. 372, No. 2 Cross Ref Long memory in intertrade durations, counts and realized volatility of NYSE stocksJournal of Statistical Planning and Inference, Vol. 140, No. 12 Cross Ref On Perturbed Random Walks14 July 2016 | Journal of Applied Probability, Vol. 47, No. 04 Cross Ref On Perturbed Random Walks14 July 2016 | Journal of Applied Probability, Vol. 47, No. 4 Cross Ref THE SUBEXPONENTIAL PRODUCT CONVOLUTION OF TWO WEIBULL-TYPE DISTRIBUTIONS18 May 2010 | Journal of the Australian Mathematical Society, Vol. 89, No. 2 Cross Ref Excursion sets of three classes of stable random fields1 July 2016 | Advances in Applied Probability, Vol. 42, No. 02 Cross Ref Excursion sets of three classes of stable random fields1 July 2016 | Advances in Applied Probability, Vol. 42, No. 2 Cross Ref Heavy Tails15 May 2010 Cross Ref Uniform tail asymptotics for the stochastic present value of aggregate claims in the renewal risk modelInsurance: Mathematics and Economics, Vol. 46, No. 2 Cross Ref High-level dependence in time series models22 April 2009 | Extremes, Vol. 13, No. 1 Cross Ref Limit Conditional Distributions for Bivariate Vectors with Polar RepresentationStochastic Models, Vol. 26, No. 1 Cross Ref Asymptotic results for sample autocovariance functions and extremes of integrated generalized Ornstein–Uhlenbeck processesBernoulli, Vol. 16, No. 1 Cross Ref Estimation for a longitudinal linear model with measurement errorsElectronic Journal of Statistics, Vol. 4, No. none Cross Ref Correlation Under Stress in Normal Variance Mixture ModelsSSRN Electronic Journal Cross Ref Second order properties of distribution tails and estimation of tail exponents in random difference equations17 March 2009 | Extremes, Vol. 12, No. 4 Cross Ref Uniform Estimate for Maximum of Randomly Weighted Sums with Applications to Ruin Theory8 July 2008 | Methodology and Computing in Applied Probability, Vol. 11, No. 4 Cross Ref Randomly Weighted Sums of Negatively Associated Random Variables with Heavy Tails Cross Ref The extremogram: A correlogram for extreme eventsBernoulli, Vol. 15, No. 4 Cross Ref Random recurrence equations and ruin in a Markov-dependent stochastic economic environmentThe Annals of Applied Probability, Vol. 19, No. 4 Cross Ref Extremes of autoregressive threshold processes1 July 2016 | Advances in Applied Probability, Vol. 41, No. 2 Cross Ref Regularly varying multivariate time seriesStochastic Processes and their Applications, Vol. 119, No. 4 Cross Ref Throughput Scaling Laws for Wireless Ad Hoc Networks with Relay Selection Cross Ref Inverse problems for regular variation of linear filters, a cancellation property for σ-finite measures and identification of stable lawsThe Annals of Applied Probability, Vol. 19, No. 1 Cross Ref Probabilistic Properties of Stochastic Volatility Models10 February 2009 Cross Ref Extremes of Continuous–Time Processes.10 February 2009 Cross Ref Extreme Value Theory for GARCH Processes10 February 2009 Cross Ref Estimation of the autoregression parameter with infinite dispersion of noise8 February 2009 | Automation and Remote Control, Vol. 70, No. 1 Cross Ref Professor Zipf Goes to Wall StreetSSRN Electronic Journal Cross Ref Tail probabilities for infinite series of regularly varying random vectorsBernoulli, Vol. 14, No. 3 Cross Ref Tail behaviour and extremes of two-state Markov-switching autoregressive modelsComputers & Mathematics with Applications, Vol. 55, No. 12 Cross Ref Extreme value theory for space–time processes with heavy-tailed distributionsStochastic Processes and their Applications, Vol. 118, No. 4 Cross Ref Tail behavior of random products and stochastic exponentialsStochastic Processes and their Applications, Vol. 118, No. 3 Cross Ref The influence of dependence on data network models1 July 2016 | Advances in Applied Probability, Vol. 40, No. 01 Cross Ref The influence of dependence on data network models1 July 2016 | Advances in Applied Probability, Vol. 40, No. 1 Cross Ref Asymptotic behavior of the supremum tail probability for anomalous diffusionsPhysica A: Statistical Mechanics and its Applications, Vol. 387, No. 2-3 Cross Ref Asymptotics for duration-driven long range dependent processesJournal of Econometrics, Vol. 141, No. 2 Cross Ref On a Theorem of Breiman and a Class of Random Difference Equations14 July 2016 | Journal of Applied Probability, Vol. 44, No. 04 Cross Ref On a Theorem of Breiman and a Class of Random Difference Equations14 July 2016 | Journal of Applied Probability, Vol. 44, No. 4 Cross Ref The ratio of the extreme to the sum in a random sequence24 October 2007 | Extremes, Vol. 10, No. 4 Cross Ref On the extremes of a class of non-linear processes with heavy tailed innovationsNonlinear Analysis: Theory, Methods & Applications, Vol. 67, No. 7 Cross Ref Processor sharing: A survey of the mathematical theoryAutomation and Remote Control, Vol. 68, No. 9 Cross Ref Asymptotics for Ratios with Applications to Reinsurance29 March 2007 | Methodology and Computing in Applied Probability, Vol. 9, No. 2 Cross Ref A non-increasing Lindley-type equation23 May 2007 | Queueing Systems, Vol. 56, No. 1 Cross Ref Resource allocation in multicell wireless networks: Some capacity scaling laws Cross Ref Tail behavior of conditional sojourn times in Processor-Sharing queues29 December 2006 | Queueing Systems, Vol. 55, No. 2 Cross Ref On the uniqueness of the maximum of the paths of random walksJournal of Statistical Planning and Inference, Vol. 137, No. 3 Cross Ref Extremal behavior of stochastic integrals driven by regularly varying Lévy processesThe Annals of Probability, Vol. 35, No. 1 Cross Ref Cluster Sets of Self-Normalized Sums23 November 2006 | Journal of Theoretical Probability, Vol. 19, No. 4 Cross Ref ON THE TAIL BEHAVIORS OF A FAMILY OF GARCH PROCESSES30 August 2006 | Econometric Theory, Vol. 22, No. 05 Cross Ref On the regular variation of elliptical random vectorsStatistics & Probability Letters, Vol. 76, No. 14 Cross Ref On the tail behaviors of Box-Cox transformed threshold GARCH(1,1) processStatistics & Probability Letters, Vol. 76, No. 13 Cross Ref Extreme dependence of multivariate catastrophic lossesScandinavian Actuarial Journal, Vol. 2006, No. 4 Cross Ref Tail Probabilities of Randomly Weighted Sums of Random Variables with Dominated Variation2 September 2006 | Stochastic Models, Vol. 22, No. 2 Cross Ref On a Mixture GARCH Time-Series ModelJournal of Time Series Analysis, Vol. 27, No. 4 Cross Ref Sojourn time asymptotics in processor-sharing queuesQueueing Systems, Vol. 53, No. 1-2 Cross Ref Data network models of burstiness1 July 2016 | Advances in Applied Probability, Vol. 38, No. 02 Cross Ref On a random-coefficient AR(1) process with heavy-tailed renewal switching coefficient and heavy-tailed noise14 July 2016 | Journal of Applied Probability, Vol. 43, No. 02 Cross Ref Data network models of burstiness1 July 2016 | Advances in Applied Probability, Vol. 38, No. 2 Cross Ref On a random-coefficient AR(1) process with heavy-tailed renewal switching coefficient and heavy-tailed noise14 July 2016 | Journal of Applied Probability, Vol. 43, No. 2 Cross Ref Institutional Investors and Stock Market VolatilityThe Quarterly Journal of Economics, Vol. 121, No. 2 Cross Ref Limit Theorems for Moving Averages with Random Coefficients and Heavy-Tailed Noise14 July 2016 | Journal of Applied Probability, Vol. 43, No. 1 Cross Ref Stable limits of martingale transforms with application to the estimation of GARCH parametersThe Annals of Statistics, Vol. 34, No. 1 Cross Ref Regularly varying functionsPublications de l'Institut Mathematique, Vol. 80, No. 94 Cross Ref Extremal stochastic integrals: a parallel between max-stable processes and α-stable processes1 June 2006 | Extremes, Vol. 8, No. 4 Cross Ref Extremes of regularly varying Lévy-driven mixed moving average processes1 July 2016 | Advances in Applied Probability, Vol. 37, No. 04 Cross Ref Extremes of regularly varying Lévy-driven mixed moving average processes1 July 2016 | Advances in Applied Probability, Vol. 37, No. 4 Cross Ref Renewal regime switching and stable limit lawsJournal of Econometrics, Vol. 129, No. 1-2 Cross Ref The Tail Probability of Discounted Sums of Pareto-like Losses in InsuranceScandinavian Actuarial Journal, Vol. 2005, No. 6 Cross Ref Some asymptotic results for sums of dependent random variables, with actuarial applicationsInsurance: Mathematics and Economics, Vol. 37, No. 2 Cross Ref Large deviations and ruin probabilities for solutions to stochastic recurrence equations with heavy-tailed innovationsThe Annals of Probability, Vol. 33, No. 5 Cross Ref Extremes of asymptotically spherical and elliptical random vectorsInsurance: Mathematics and Economics, Vol. 36, No. 3 Cross Ref When Does a Randomly Weighted Self-normalized Sum Converge in Distribution?Electronic Communications in Probability, Vol. 10, No. none Cross Ref The Extremal 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