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ORIE Technical Reports
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This is a collection of Technical Reports and Papers written for the field of Operations Research and Information Engineering.
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Multivariate Subexponential Distributions and Their Applications
Samorodnitsky, Gennady; Sun, Julian (20150916)We propose a new definition of a multivariate subexponential distribution. We compare this definition with the two existing notions of multivariate subexponentiality, and compute the asymptotic behaviour of the ruin ... 
Ful lling Orders in a MultiEchelon Capacitated Online Retail System: PART TWO, realtime purchasing and ful llment decision making
Li, Juan; Muckstadt, John (20150513)When ful lling customer orders, online retailers must operate their multiwarehouse systems with great care to ensure that these orders are satis ed in a timely and cost e ective manner. We worked closely with a major ... 
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 ... 
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 ... 
MultiPeriod Stock Allocation Via Robust Optimization
Jackson, Peter; Muckstadt, John (20150325)In this paper we revisit a longstanding multiechelon inventory allocation problem from a robust optimization perspective. We formulate the problem as a one warehouse, Nretailer, multiperiod, stock allocation problem ... 
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 ... 
Numerical Validation of Fill Rate Estimation Methods for Two and ThreeDemand Class Rationing Policies with OneforOne Replenishment and General Lead Time Distributions
Vicil, Oguzhan; Jackson, Peter (20150108)In this report, we conduct numerical simulations of two and threedemand class inventory threshold rationing systems under oneforone replenishment policies. The performance metrics of interest are the fill rates of the ... 
Timechanged extremal process as a random sup measure
Lacaux, Céline; Samorodnitsky, Gennady (20141009)A functional limit theorem for the partial maxima of a long memory stable sequence produces a limiting process that can be described as a betapower time change in the classical Fr\'echet extremal process, for beta ... 
Tauberian Theory for Multivariate Regularly Varying Distributions with Application to Preferential Attachment Networks
Resnick, Sidney; Samorodnitsky, Gennady (20140625)AbelTauberian theorems relate power law behavior of distributions and their transforms. We formulate and prove a multivariate version for nonstandard regularly varying measures on R_+^p and then apply it to prove ... 
Nonstandard regular variation of the indegree and the outdegree in the preferential attachement model
Samorodnitsky, Gennady; Resnick, Sidney; Towsley, Don; Davis, Richard; Willis, Amy; Wan, Phyllis (20140625)For the directed edge preferential attachment network growth model studied by Bollobas et al. (2003) and Krapivsky and Redner (2001), we prove that the joint distribution of indegree and outdegree has jointly ... 
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 ... 
Stock Optimization in Emergency Resupply Networks under Stuttering Poisson Demand
Chen, J; Jackson, P.L.; Muckstadt, J (201304)We consider a network in which field stocking locations (FSLs) manage multiple parts according to an (S1,S) policy. Demand processes for the parts are assumed to be independent stuttering Poisson processes. Regular ... 
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 ... 
Multivariate tail measure and the estimation of CoVar
Nguyen, Tilo; Samorodnitsky, Gennady (20121009)The quality of estimation of multivariate tails depends significantly on the portion of the sample included in the estimation. A simple approach involving sequential statistical testing is proposed in order to select ... 
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 ... 
Intrinsic location functionals of stationary processes
Samorodnitsky, Gennady; Shen, Yi (20120621)We consider a large family of measurable functionals of the sample path of a stochastic process over compact intervals (including first hitting times, leftmost location of the supremum, etc.) we call intrinsic ... 
On the existence of paths between points in high level excursion sets of Gaussian random fields
Adler, Robert; Moldavskaya, Elina; Samorodnitsky, Gennady (20120327)The structure of Gaussian random fields over high levels is a well researched and well understood area, particularly if the field is smooth. However, the question as to whether or not two or more points which lie in ... 
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 ... 
Latent factor regression models for grouped outcomes
Woodard, Dawn; Love, Tanzy; Thurston, Sally; Ruppert, David; Sathyanarayana, Sheela; Swan, Shanna (20120131)We consider models for the effect of exposure on multiple outcomes, where the outcomes are nested in domains. We show that random effect models for this nested situation fit into a standard factor model framework, which ... 
Weak weak quenched limits for the pathvalued processes of hitting times and positions of a transient, onedimensional random walk in a random environment
Peterson, Jonathon; Samorodnitsky, Gennady (20111215)In this article we continue the study of the quenched distributions of transient, onedimensional random walks in a random environment. In a previous article we showed that while the quenched distributions of the hitting ...