Current fluctuations for independent random walks in multiple dimensions

Consider a system of particles evolving as independent and identically distributed (i.i.d.) random walks. Initial fluctuations in the particle density get translated over time with velocity $\vec{v}$, the common mean velocity of the random walks. Consider a box centered around an observer who starts at the origin and moves with constant velocity $\vec{v}$. To observe interesting fluctuations beyond the translation of initial density fluctuations, we measure the net flux of particles over time into this moving box. We call this the ``box-current" process. We generalize this current process to a distribution valued process. Scaling time by $n$ and space by $\sqrt{n}$ gives current fluctuations of order $n^{d/4}$ where $d$ is the space dimension. The scaling limit of the normalized current process is a distribution valued Gaussian process with given covariance. The limiting current process is equal in distribution to the solution of a given stochastic partial differential equation which is related to the generalized Ornstein-Uhlenbeck process.Comment: 31 pages; accepted for publication in Journal of Theoretical Probabilit

MAPPING INDIAN DISTRICTS ACROSS CENSUS YEARS, 1971-2001

The Indian states have been the standard unit of analysis for research on India that uses official data sources. For many empirical questions, states are a natural starting point because state governments set political agendas and budgets and administer a wide range of services. In addition, the boundaries of many states have been unchanged for over half a century and those of all major states were largely unchanged between 1971 and 2000. This stability has resulted in the relatively easy construction and use of panel data sets at the state level and these data have been used to ask a variety of questions relating to the e ectiveness of public policy. The use of more disaggregated district data allows the study of outcomes across regions with similar historical contexts and political regimes. States have an average of 20 districts, so district level panels can also be much larger. Most district-level studies however have relied on cross-sectional analysis because district comparisons over time are complicated by multiple boundary changes. Between 1971 and 2001, the number of districts increased from 356 to 593, a rise of about 67%. The purpose of this paper is to provide information on boundary changes across districts that will facilitate the construction of district-level panel data sets. We use population data from the state and central volumes of the Census of India to document changes in district boundaries between 1971 and 2001. For each decade during the 1971-2001 pe- riod, we classify districts into three categories: those with unchanged boundaries, those created by partitioning existing districts and nally, districts whose current boundaries were located in multiple districts at the time of the previous census. We nd that 136 of the 356 Indian dis- tricts in 1971 (38%) were una ected by boundary changes over the subsequent three decades, 79 districts (22%) were cleanly partitioned into multiple districts over the same period, and the 1 remaining 141 districts experienced more complex changes. Unchanged districts obviously pose no problem for the construction of panel data and the number of these districts can be quite large for short panels. For partitioned districts we provide population weights that permit the construction of panels using boundaries of either later or earlier census years as the base. For districts that are neither unchanged nor partitioned it is in general only possible to generate accurate population weights across adjacent census years. We provide these weights separately for the three periods: 1971-1981, 1981-1991, and 1991-2001. In addition, we amalgamate neigh- bouring districts into composite regions with unchanged boundaries between each census year and 2001. These composite regions, along with the unchanged and partitioned districts, give us the complete set of geographical units with unchanged boundaries between any census year and 2001. The following section provides details on data sources and our methods and compares these to those used by other studies relying on multi-year district data. Section 3 summarises some basic patterns. Section 4 concludes with some caveats on using our data and points to the type of work needed to construct district-level series over long time periods.

Small-time asymptotics for fast mean-reverting stochastic volatility models

In this paper, we study stochastic volatility models in regimes where the maturity is small, but large compared to the mean-reversion time of the stochastic volatility factor. The problem falls in the class of averaging/homogenization problems for nonlinear HJB-type equations where the "fast variable" lives in a noncompact space. We develop a general argument based on viscosity solutions which we apply to the two regimes studied in the paper. We derive a large deviation principle, and we deduce asymptotic prices for out-of-the-money call and put options, and their corresponding implied volatilities. The results of this paper generalize the ones obtained in Feng, Forde and Fouque [SIAM J. Financial Math. 1 (2010) 126-141] by a moment generating function computation in the particular case of the Heston model.Comment: Published in at http://dx.doi.org/10.1214/11-AAP801 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Signals for R-parity-violating Supersymmetry at a 500 GeV e+ e- Collider

We investigate the production of charginos and neutralinos at a 500 GeV e^+e^- collider (NLC) and study their decays to the lightest neutralino, which then decays into multi-fermion final states through couplings which do not conserve R-parity. These couplings are assumed to affect only the decay of the lightest neutralino. Detailed analyses of the possible signals and backgrounds are performed for five selected points in the parameter space.Comment: 42 pages, LaTeX, 12 postscript figure

Safe drinking water for rural populations in India: An effective service delivery model by Naandi Foundation

This articles analyses how Naandi Foundation has evolved a community-based model in which a water treatment plant is set up in a village after testing the available source of water for nature of contamination. Using appropriate treatment technology, this plant (which is designed to cover the entire village population) is operational for 5 to 8 hours every day and residents of the village are mobilised to collect their daily household’s need of drinking water from here at a nominal user-fee of Rs 4 (USD 0.08) for 20 litres. The model engages the water bureaucracy, political representatives and local self government in rollout of safe water services in a village. This new service delivery design, which combines public, private and community contributions for provision of safe drinking water at a very low at a nominal user fee, at the same time exploring modalities of access to this water by the poorest of the village has been the innovative feature of Naandi’s strategy.Cet article analyse la manière dont la Fondation Naandi a développé un modèle communautaire qui consiste à mettre en place une usine de traitement de l'eau dans un village après analyse de la nature de la contamination de la source d'eau disponible. Grâce à une technologie de traitement appropriée, cette usine (conçue pour couvrir l'ensemble de la population du village) est opérationnelle pendant 5 à 8 heures par jour et les villageois peuvent venir chercher la ration d'eau potable quotidienne de leur foyer pour un montant nominal de 4 Rs (0,05 €) pour 20 litres. Dans ce modèle, de nombreux acteurs dont les responsables politiques et le gouvernement local participent au déploiement des services d'eau saine dans un village. Cette nouvelle conception de prestation de services, qui associe des contributions publiques, privées et communautaires pour la fourniture d'eau potable saine pour un montant nominal très bas, et qui explore les modalités d'accès à l'eau pour les villages les plus pauvres, constitue l'aspect novateur de la stratégie de la Fondation Naandi.El presente artículo analiza el modo en que Naandi Foundation ha mejorado un modelo basado en la comunidad en el que se instala una planta de tratamiento de aguas en una aldea tras comprobar la naturaleza de la contaminación existente en la fuente de agua disponible. Esta planta, diseñada para cubrir las necesidades de toda la población local, utiliza una tecnología de tratamiento adecuada y funciona entre 5 y 8 horas al día. Los residentes de la aldea se movilizan para recoger la cantidad diaria necesaria para cubrir sus necesidades de agua potable, a una tarifa de 4 rupias (0,08 USD) por 20 litros. El modelo reúne a la burocracia del agua, la representación política y el autogobierno local para dar a conocer los servicios de agua segura en la aldea. Este nuevo diseño de prestación de servicios, que combina las contribuciones públicas, privadas y comunitarias para la provisión de agua potable segura a una tasa nominal muy baja para el usuario al tiempo que explora las modalidades de acceso a la misma por parte de los más desfavorecidos de la aldea, ha sido la característica más innovadora de la estrategia de Naandi

Effect of CBR, FTP and FTP GENERIC Traffic Patterns on the Performance of Routing Protocols in MANET

In recent years mobile ad hoc networks have become very popular and lots of research is being done on different aspects of MANET. Mobile ad hoc network (MANET) is a wireless network without infrastructure. In this paper, an attempt has been made to evaluate the performance of two well known routing protocols AODV and DSR .Three traffic patterns CBR, FTP and FTP GENERIC are used to check the performance of routing protocols ( AODV,DSR) with various metrics like as Packet Delivery Ratio and throughput using GLoMoSIM (Global Mobile information systems simulation)