http://hdl.handle.net/1813/525 Wed, 22 May 2013 13:15:40 GMT 2013-05-22T13:15:40Z http://ecommons.library.cornell.edu:80/retrieve/3389/24.gif http://hdl.handle.net/1813/525 http://hdl.handle.net/1813/33186 Title: Stock Optimization in Emergency Resupply Networks under Stuttering Poisson Demand Authors: Chen, J; Jackson, P.L.; Muckstadt, J Abstract: We consider a network in which field stocking locations (FSLs) manage multiple parts according to an (S-1,S) policy. Demand processes for the parts are assumed to be independent stuttering Poisson processes. Regular replenishments to an FSL occur from a regional stocking location (RSL) that has an unlimited supply of each part type. Demand in excess of supply at an FSL is routed to an emergency stocking location (ESL), which also employs an (S-1,S) policy to manage its inventory. Demand in excess of supply at the ESL is backordered. Lead time from the ESL to each FSL is assumed to be negligible compared to the RSL-ESL resupply time. In companion papers we have shown how to approximate the joint probability distributions of units on hand, units in regular resupply, and units in emergency resupply. In this paper, we focus on the problem of determining the stock levels at the FSLs and ESL across all part numbers that minimize backorder, and emergency resupply costs subject to an inventory investment budget constraint. The problem is shown to be a nonconvex integer programming problem, and we explore a collection of heuristics for solving the optimization problem. Mon, 01 Apr 2013 00:00:00 GMT http://hdl.handle.net/1813/33186 2013-04-01T00:00:00Z http://hdl.handle.net/1813/31540 Title: Calculation of ruin probabilities for a dense class of heavy tailed distributions Authors: Bladt, Mogens; Nielsen, Bo Friis; Samorodnitsky, Gennady Abstract: In this paper we propose a class of infinite--dimensional phase--type distributions with finitely many parameters as models for heavy tailed distributions. The class of finite--dimensional distributions is dense in the class of distributions on the positive reals and may hence approximate any such distribution. We prove that formulas from renewal theory, and with a particular attention to ruin probabilities, which are true for common phase--type distributions also hold true for the infinite--dimensional case. We provide algorithms for calculating functionals of interest such as the renewal density and the ruin probability. It might be of interest to approximate a given heavy--tailed distribution of some other type by a distribution from the class of infinite--dimensional phase--type distributions and to this end we provide a calibration procedure which works for the approximation of distributions with a slowly varying tail. An example from risk theory, comparing ruin probabilities for a classical risk process with Pareto distributed claim sizes, is presented and exact known ruin probabilities for the Pareto case are compared to the ones obtained by approximating by an infinite--dimensional hyper--exponential distribution. Tue, 05 Mar 2013 00:00:00 GMT http://hdl.handle.net/1813/31540 2013-03-05T00:00:00Z http://hdl.handle.net/1813/30442 Title: Multivariate tail measure and the estimation of CoVar Authors: Nguyen, Tilo; Samorodnitsky, Gennady Abstract: 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 which observations should be used for estimation of the tail and spectral measures. We prove that the estimator is consistent. We test the proposed method on simulated data, and subsequently apply it to analyze CoVar for stock and index returns. Tue, 09 Oct 2012 00:00:00 GMT http://hdl.handle.net/1813/30442 2012-10-09T00:00:00Z http://hdl.handle.net/1813/29996 Title: Functional Central Limit Theorem for Heavy Tailed Stationary Infinitely Divisible Processes Generated by Conservative Flows Authors: Owada, Takashi; Samorodnitsky, Gennady Abstract: 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 stable self-similar processes with stationary increments, that coincides on a part of its parameter space with a previously described process. The normalizing sequence and the limiting process are determined by the ergodic theoretical properties of the flow underlying the integral representation of the process. These properties can be interpreted as determining how long is the memory of the stationary infinitely divisible process. We also establish functional convergence, in a strong distributional sense, for conservative pointwise dual ergodic maps preserving an infinite measure. Tue, 18 Sep 2012 00:00:00 GMT http://hdl.handle.net/1813/29996 2012-09-18T00:00:00Z http://hdl.handle.net/1813/29085 Title: Intrinsic location functionals of stationary processes Authors: Samorodnitsky, Gennady; Shen, Yi Abstract: 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 location functionals. Despite the large variety of these functionals and their different nature, we show that for stationary processes the distribution of any intrinsic location functional over an interval is absolute continuous in the interior of the interval, and the density functions always have a version satisfying the same total variation constraints. Conversely, these total variation constraints are shown to actually characterize stationarity of the underlying stochastic process. We also show that the possible distributions of the intrinsic location functionals over an interval form a weakly closed convex set and describe its extreme points, and present applications of this description. Thu, 21 Jun 2012 00:00:00 GMT http://hdl.handle.net/1813/29085 2012-06-21T00:00:00Z http://hdl.handle.net/1813/28637 Title: On the existence of paths between points in high level excursion sets of Gaussian random fields Authors: Adler, Robert; Moldavskaya, Elina; Samorodnitsky, Gennady Abstract: 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 an excursion set belong to the same connected component has constantly eluded analysis. We study this problem from the point of view of large deviations, finding the asymptotic probabilities that two such points are connected by a path laying within the excursion set, and so belong to the same component. In addition, we obtain a characterization and descriptions of the most likely paths, given that one exists. Tue, 27 Mar 2012 00:00:00 GMT http://hdl.handle.net/1813/28637 2012-03-27T00:00:00Z http://hdl.handle.net/1813/28598 Title: Fractional moments of solutions to stochastic recurrence equations Authors: Mikosch, Thomas; Samorodnitsky, Gennady; Tafakori, Laleh Abstract: 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 additive term has an Erlang distribution. We provide various approximations to the moments and show their performance in a small numerical study Tue, 13 Mar 2012 00:00:00 GMT http://hdl.handle.net/1813/28598 2012-03-13T00:00:00Z http://hdl.handle.net/1813/28480 Title: Latent factor regression models for grouped outcomes Authors: Woodard, Dawn; Love, Tanzy; Thurston, Sally; Ruppert, David; Sathyanarayana, Sheela; Swan, Shanna Abstract: 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 leads us to view the modeling options as a spectrum between parsimonious random effect multiple outcomes models and more general continuous latent factor models. We introduce a set of models along this spectrum that extend an existing random effect model for multiple outcomes nested in domains. We characterize the tradeoffs between parsimony and flexibility in this set of models, applying them to both simulated data and data relating phthalate exposure to infant anthropometry. Tue, 31 Jan 2012 00:00:00 GMT http://hdl.handle.net/1813/28480 2012-01-31T00:00:00Z http://hdl.handle.net/1813/28221 Title: Weak weak quenched limits for the path-valued processes of hitting times and positions of a transient, one-dimensional random walk in a random environment Authors: Peterson, Jonathon; Samorodnitsky, Gennady Abstract: In this article we continue the study of the quenched distributions of transient, one-dimensional random walks in a random environment. In a previous article we showed that while the quenched distributions of the hitting times do not converge to any deterministic distribution, they do have a weak weak limit in the sense that - viewed as random elements of the space of probability measures - they converge in distribution to a certain random probability measure (we refer to this as a weak weak limit because it is a weak limit in the weak topology). Here, we improve this result to the path-valued process of hitting times. As a consequence, we are able to also prove a weak weak quenched limit theorem for the path of the random walk itself. Thu, 15 Dec 2011 00:00:00 GMT http://hdl.handle.net/1813/28221 2011-12-15T00:00:00Z http://hdl.handle.net/1813/24397 Title: Distribution of the supremum location of stationary processes Authors: Samorodnitsky, Gennady; Shen, Yi Abstract: 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 of such stationary processes. We show that, in the strongly mixing case, this distribution does tend to the uniform in a certain sense as the length of the interval increases to infinity. Fri, 07 Oct 2011 00:00:00 GMT http://hdl.handle.net/1813/24397 2011-10-07T00:00:00Z