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Browsing by Author "Samorodnitsky, Gennady"
Now showing items 120 of 48

Asymptotic behaviour of Gaussian minima
Chakrabarty, Arijit; Samorodnitsky, Gennady (2016)We investigate what happens when an entire sample path of a smooth Gaussian process on a compact interval lies above a high level. Specifically, we determine the precise asymptotic probability of such an event, the ... 
Asymptotic Normality of Degree Counts in a Preferential Attachment Model
Resnick, Sidney; Samorodnitsky, Gennady (20150428)Preferential attachment is a widely adopted paradigm for understanding the dynamics of social networks. Formal statistical inference, for instance GLM techniques, and model verification methods will require knowing ... 
Bayesian Methods For Uncertainty Quantification
Bilionis, Ilias (20130526)Computer codes simulating physical systems usually have responses that consist of a set of distinct outputs (e.g., velocity and pressure) that evolve also in space and time and depend on many unknown input parameters (e.g., ... 
Calculation of ruin probabilities for a dense class of heavy tailed distributions
Bladt, Mogens; Nielsen, Bo Friis; Samorodnitsky, Gennady (20130305)In this paper we propose a class of infinitedimensional phasetype distributions with finitely many parameters as models for heavy tailed distributions. The class of finitedimensional distributions is dense ... 
Climbing down Gaussian peaks
Adler, Robert; Samorodnitsky, Gennady (20150128)How likely is the high level of a continuous Gaussian random field on an Euclidean space to have a ``hole'' of a certain dimension and depth? Questions of this type are difficult, but in this paper we make progress on ... 
Contact distribution in a thinned Boolean model with power law radii
Dong, Yinghua; Samorodnitsky, Gennady (201603)We consider a weighted stationary spherical Boolean model in R^d. Assuming that the radii of the balls in the Boolean model have regularly varying tails, we establish the asymptotic behaviour of the tail of the contact ... 
Distribution of the supremum location of stationary processes
Samorodnitsky, Gennady; Shen, Yi (20111007)The location of the unique supremum of a stationary process on an interval does not need to be uniformly distributed over that interval. We describe all possible distributions of the supremum location for a broad class ... 
Do financial returns have finite or infinite variance? A paradox and an explanantion
Grabchak, Michael; Samorodnitsky, Gennady (20090804)One of the major points of contention in studying and modeling financial returns is whether or not the variance of the returns is finite or infinite (sometimes referred to as the BachelierSamuelson Gaussian world versus ... 
An Efficient Computational Framework For Uncertainty Quantification In Multiscale Systems
Ma, Xiang (20110131)To accurately predict the performance of physical systems, it becomes essential for one to include the effects of input uncertainties into the model system and understand how they propagate and alter the final solution. ... 
Ergodic Theoretical Approach To Investigate Memory Properties Of Heavy Tailed Processes
Owada, Takashi (20130819)A class of infinitely divisible processes includes not only wellknown L´ vy processes, e but also a wide variety of processes such as the Gaussian and the stable processes, moving averages driven by L´ vy processes (e.g., ... 
Excursion Sets Of Stable Random Fields
Adler, Robert J.; Samorodnitsky, Gennady; Taylor, Jonathan E. (20080118)Studying the geometry generated by Gaussian and Gaussianrelated random fields via their excursion sets is now a well developed and well understood subject. The purely nonGaussian scenario has, however, not been studied ... 
Extremal Properties Of Markov Chains And The Conditional Extreme Value Model
Zeber, David (20120820)Multivariate extreme value theory has proven useful for modeling multivariate data in fields such as finance and environmental science, where one is interested in accounting for the tendency of observations to exceed an ... 
Extreme values of the uniform autoregressive processes and missing observations
Glavas, Lenka; Mladenovic, Pavle; Samorodnitsky, Gennady (2016)We investigate partial maxima of the uniform AR(1) processes with parameter r geq 2. Positively and negatively correlated processes are considered. New limit theorems for maxima in complete and incomplete samples are obtained 
Fractional moments of solutions to stochastic recurrence equations
Mikosch, Thomas; Samorodnitsky, Gennady; Tafakori, Laleh (20120313)In this paper we study the fractional moments of the stationary solution to a stochastic recursion. We derive recursive formulas for the fractional moments of the solution. Special attention is given to the case when the ... 
Functionindexed empirical processes based on an infinite source Poisson transmission stream
Roueff, Francois; Samorodnitsky, Gennady; Soulier, Philippe (20100408)We study the asymptotic behavior of empirical processes generated by measurable bounded functions of an infinite source Poisson transmission process when the session length have infinite variance. In spite of the ... 
Functional central limit theorem for negatively dependent heavytailed stationary infinitely divisible processes generated by conservative flows
Jung, Paul; Owada, Takashi; Samorodnitsky, Gennady (20150406)We prove a functional central limit theorem for partial sums of symmetric stationary long range dependent heavy tailed infinitely divisible processes with a certain type of negative dependence. Previously only positive ... 
Functional Central Limit Theorem for Heavy Tailed Stationary Infinitely Divisible Processes Generated by Conservative Flows
Owada, Takashi; Samorodnitsky, Gennady (20120918)We establish a new class of functional central limit theorems for partial sum of certain symmetric stationary infinitely divisible processes with regularly varying Levy measures. The limit process is a new class of symmetric ... 
General inverse problems for regular variation
Damek, Ewa; Mikosch, Thomas; Rosinski, Jan; Samorodnitsky, Gennady (20131002)Regular variation of distributional tails is known to be preserved by various linear transformations of some random structures. An inverse problem for regular variation aims at understanding whether the regular ... 
High level excursion set geometry for nonGaussian infinitely divisible random fields
Adler, Robert; Samorodnitsky, Gennady; Taylor, Jonathan (20090804)We consider smooth, infinitely divisible random fields with regularly varying Levy measure, and are interested in the geometric characteristics of the excursion sets over high levels u. For a large class of such ... 
How Fast Can the ChordLength Distribution Decay?
Demichel, Yann; Estrade, Anne; Kratz, Marie; Samorodnitsky, Gennady (20090921)The modelling of random biphasic, or porous, media has been, and still is, under active investigation by mathematicians, physicists or physicians. In this paper we consider a thresholded random process X as a source of ...