AR(1) sequence with random coefficients: Regenerative properties and its application

Let $\{X_n\}_{n\ge0}$ be a sequence of real valued random variables such that $X_n=\rho_n X_{n-1}+\epsilon_n,~n=1,2,\ldots$, where $\{(\rho_n,\epsilon_n)\}_{n\ge1}$ are i.i.d. and independent of initial value (possibly random) $X_0$. In this paper it is shown that, under some natural conditions on the distribution of $(\rho_1,\epsilon_1)$, the sequence $\{X_n\}_{n\ge0}$ is regenerative in the sense that it could be broken up into i.i.d. components. Further, when $\rho_1$ and $\epsilon_1$ are independent, we construct a non-parametric strongly consistent estimator of the characteristic functions of $\rho_1$ and $\epsilon_1$

Critical age-dependent branching Markov processes and their scaling limits

This paper studies: (i) the long-time behaviour of the empirical distribution of age and normalized position of an age-dependent critical branching Markov process conditioned on non-extinction; and (ii) the super-process limit of a sequence of age dependent critical branching Brownian motions

A Queueing System for Modeling a File Sharing Principle

International audienceWe investigate in this paper the performance of a simple file sharing principle. For this purpose, we consider a system composed of N peers becoming active at exponential random times; the system is initiated with only one server offering the desired file and the other peers after becoming active try to download it. Once the file has been downloaded by a peer, this one immediately becomes a server. To investigate the transient behavior of this file sharing system, we study the instant when the system shifts from a congested state where all servers available are saturated by incoming demands to a state where a growing number of servers are idle. In spite of its apparent simplicity, this queueing model (with a random number of servers) turns out to be quite difficult to analyze. A formulation in terms of an urn and ball model is proposed and corresponding scaling results are derived. These asymptotic results are then compared against simulations

On the Spectral Index of Distant Radio Galaxies

The problems of using the spectral index of radio galaxies in various tests, in particular, in selecting distant radio sources are considered. The history of the question of choosing a criterion of searching for distant radio galaxies based on the spectral index is presented. For a new catalog of 2442 radio galaxies constructed from NED, SDSS, and CATS data, an analytical form of the sp ectral index.redshift relation has been determined for the first time. The spectral index.angular size and spectral index.flux density diagrams have also been constructed. Peculiarities of the distribution of sources on these diagrams are discussed.Comment: 7 pages,5 figure

Second round statewide sentinel-based population survey for estimation of the burden of active infection and anti-SARS-CoV-2 IgG antibodies in the general population of Karnataka, India, during January-February 2021

Objective Demonstrate the feasibility of using the existing sentinel surveillance infrastructure to conduct the second round of the serial cross-sectional sentinel-based population survey. Assess active infection, seroprevalence, and their evolution in the general population across Karnataka. Identify local variations for locally appropriate actions. Additionally, assess the clinical sensitivity of the testing kit used on account of variability of antibody levels in the population. Methods The cross-sectional study of 41,228 participants across 290 healthcare facilities in all 30 districts of Karnataka was done among three groups of participants (low, moderate, and high-risk). The geographical spread was sufficient to capture local variations. Consenting participants were subjected to real-time reverse transcription-polymerase chain reaction (RT-PCR) testing, and antibody (IgG) testing. Clinical sensitivity was assessed by conducting a longitudinal study among participants identified as COVID-19 positive in the first survey round. Results Overall weighted adjusted seroprevalence of IgG was 15.6% (95% CI: 14.9–16.3), crude IgG prevalence was 15.0% and crude active infection was 0.5%. Statewide infection fatality rate (IFR) was estimated as 0.11%, and COVID-19 burden estimated between 26.1 to 37.7% (at 90% confidence). Further, Cases-to-infections ratio (CIR) varied 3-35 across units and IFR varied 0.04–0.50% across units. Clinical sensitivity of the IgG ELISA test kit was estimated as ≥38.9%. Conclusion We demonstrated the feasibility and simplicity of sentinel-based population survey in measuring variations in subnational and local data, useful for locally appropriate actions in different locations. The sentinel-based population survey thus helped identify districts that needed better testing, reporting, and clinical management. The state was far from attaining natural immunity during the survey and hence must step up vaccination coverage and enforce public health measures to prevent the spread of COVD-19.The Institutional Ethics Committee (IEC) of the Indian Institute of Public Health - Bengaluru campus reviewed and approved the study (vide. IIPHHB/TRCIEC/174/2020) and the subsequent change of protocol to perform the longitudinal study (vide PHFI/IIPH-BLR/076/2020-21). We informed the participants of the purpose of the surveys, how the samples would be taken and requested them to respond to the screening questions. After obtaining informed consent, we noted basic demographic details, exposure history, symptoms observed in the previous month, and clinical history. Participants' test results were shared with them by the concerned healthcare facility.Scopu

Modified Bessel function asymptotics via probability

Using the local and global versions of the central limit theorem it is shown that, for the modified Bessel function I[varrho](x), , .33A 60F modified Bessel function central limit theorem asymptotics

Modified bessel function asymptotics via probability

Using the local and global versions of the central limit theorem it is shown that, for the modified Bessel function I<SUB>&#961;</SUB>(x). (i) for fixed &#961;. I<SUB>&#961;</SUB>(x)e<SUP>-</SUP> &#8730;x &#8594; (&#8730;2&#960;)<SUP>-</SUP> as x &#8594; &#8734; (ii) I<SUB>&#945;(x)</SUB> &#8730;xe<SUP>-</SUP> &#8594; (&#8730;2&#960;)<SUP>-1</SUP> e<SUP>-&#945;<SUP>2</SUP>&#946; </SUP>and &#931;<SUB>0&#8805;j&#8805;&#945;(x)</SUB> I<SUB>j</SUB>(x)e<SUP>-x</SUP> &#8594; &#934;(&#945;) - 2<SUP>-1</SUP> if &#945;(x)/&#8730;x &#8594; &#945; .0 &#8805; &#945; &lt; &#8734; as x &#8594; &#8734;