Convergence of functionals of sums of r.v.s to local times of fractional stable motions

Consider a sequence X_k=\sum_{j=0}^{\infty}c_j\xi_{k-j}, k\geq 1, where c_j, j\geq 0, is a sequence of constants and \xi_j, -\infty <j<\infty, is a sequence of independent identically distributed (i.i.d.) random variables (r.v.s) belonging to the domain of attraction of a strictly stable law with index 0<\alpha \leq 2. Let S_k=\sum_{j=1}^kX_j. Under suitable conditions on the constants c_j it is known that for a suitable normalizing constant \gamma_n, the partial sum process \gamma_n^{-1}S_{[nt]} converges in distribution to a linear fractional stable motion (indexed by \alpha and H, 0<H<1). A fractional ARIMA process with possibly heavy tailed innovations is a special case of the process X_k. In this paper it is established that the process n^{-1}\beta_n\sum_{k=1}^{[nt]}f(\beta_n(\gamma_n^{-1}S_k+x)) converges in distribution to (\int_{-\infty}^{\infty}f(y) dy)L(t,-x), where L(t,x) is the local time of the linear fractional stable motion, for a wide class of functions f(y) that includes the indicator functions of bounded intervals of the real line. Here \beta_n\to \infty such that n^{-1}\beta_n\to 0. The only further condition that is assumed on the distribution of \xi_1 is that either it satisfies the Cram\'er's condition or has a nonzero absolutely continuous component. The results have motivation in large sample inference for certain nonlinear time series models.Comment: Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/00911790400000065

Limit Theorems for Functionals of Sums That Converge to Fractional Stable Motions

Too technical to post here. Please see paper.

Hyperspectral and Hypertemporal Longwave Infrared Data Characterization

The Army Research Lab conducted a persistent imaging experiment called the Spectral and Polarimetric Imagery Collection Experiment (SPICE) in 2012 and 2013 which focused on collecting and exploiting long wave infrared hyperspectral and polarimetric imagery. A part of this dataset was made for public release for research and development purposes. This thesis investigated the hyperspectral portion of this released dataset through data characterization and scene characterization of man-made and natural objects. First, the data were contrasted with MODerate resolution atmospheric TRANsmission (MODTRAN) results and found to be comparable. Instrument noise was characterized using an in-scene black panel, and was found to be comparable with the sensor manufacturer\u27s specication. The temporal and spatial variation of certain objects in the scene were characterized. Temporal target detection was conducted on man-made objects in the scene using three target detection algorithms: spectral angle mapper (SAM), spectral matched lter (SMF) and adaptive coherence/cosine estimator (ACE). SMF produced the best results for detecting the targets when the training and testing data originated from different time periods, with a time index percentage result of 52.9%. Unsupervised and supervised classication were conducted using spectral and temporal target signatures. Temporal target signatures produced better visual classication than spectral target signature for unsupervised classication. Supervised classication yielded better results using the spectral target signatures, with a highest weighted accuracy of 99% for 7-class reference image. Four emissivity retrieval algorithms were applied on this dataset. However, the retrieved emissivities from all four methods did not represent true material emissivity and could not be used for analysis. This spectrally and temporally rich dataset enabled to conduct analysis that was not possible with other data collections. Regarding future work, applying noise-reduction techniques before applying temperature-emissivity retrieval algorithms may produce more realistic emissivity values, which could be used for target detection and material identification

Linear retrial inventory system with second optional service under mixed priority service

The present paper deals with a generalization of the homogeneous single server finite source retrial inventory system with two classes of customers - one with high priority customer and the other with low priority customer. The inventory is replenished according to an (s, Q) policy and the replenishing times are assumed to be exponentially distributed. The server provides two types of services - one with essential service and the other with a second optional service. The service times of the 1st (essential) and 2nd (optional) services are independent and exponentially distributed. The high priority customers have a mixed priority over the low priority customers. Retrial is introduced for low priority customers only. The joint probability distribution of the number of customers in the waiting hall, the number of customers in the orbit and the inventory level is obtained for the steady state case. Some important system performance measures in the steady state are derived and the long-run total expected cost rate is also derived.Publisher's Versio