eCommons Community:
http://hdl.handle.net/1813/525
2014-04-23T10:44:25ZGeneral inverse problems for regular variation
http://hdl.handle.net/1813/34411
Title: General inverse problems for regular variation
Authors: Damek, Ewa; Mikosch, Thomas; Rosinski, Jan; Samorodnitsky, Gennady
Abstract: 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 variation of a
transformed random object is caused by regular variation of components
of the original random structure. In this paper we build up on previous
work and derive results in the multivariate case and in
situations where regular variation is
not restricted to one particular direction or quadrant.2013-10-02T00:00:00ZStock Optimization in Emergency Resupply Networks under Stuttering Poisson Demand
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.2013-04-01T00:00:00ZCalculation of ruin probabilities for a dense class of heavy tailed distributions
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.2013-03-05T00:00:00ZMultivariate tail measure and the estimation of CoVar
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.2012-10-09T00:00:00ZFunctional Central Limit Theorem for Heavy Tailed Stationary Infinitely Divisible Processes Generated by Conservative Flows
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.2012-09-18T00:00:00ZIntrinsic location functionals of stationary processes
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.2012-06-21T00:00:00ZOn the existence of paths between points in high level excursion sets of Gaussian random fields
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.2012-03-27T00:00:00ZFractional moments of solutions to stochastic recurrence equations
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 study2012-03-13T00:00:00ZLatent factor regression models for grouped outcomes
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.2012-01-31T00:00:00ZWeak weak quenched limits for the path-valued processes of hitting times and positions of a transient, one-dimensional random walk in a random environment
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.2011-12-15T00:00:00Z