The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Harpreet S. Dhillon - One of the best experts on this subject based on the ideXlab platform.
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shortest path distance in manhattan poisson line Cox Process
Journal of Statistical Physics, 2020Co-Authors: Vishnu Vardhan Chetlur, Harpreet S. Dhillon, Carl P DettmannAbstract:While the Euclidean distance characteristics of the Poisson line Cox Process (PLCP) have been investigated in the literature, the analytical characterization of the path distances is still an open problem. In this paper, we solve this problem for the stationary Manhattan Poisson line Cox Process (MPLCP), which is a variant of the PLCP. Specifically, we derive the exact cumulative distribution function (CDF) for the length of the shortest path to the nearest point of the MPLCP in the sense of path distance measured from two reference points: (i) the typical intersection of the Manhattan Poisson line Process (MPLP), and (ii) the typical point of the MPLCP. We also discuss the application of these results in infrastructure planning, wireless communication, and transportation networks.
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on the k nearest neighbor path distance from the typical intersection in the manhattan poisson line Cox Process
arXiv: Networking and Internet Architecture, 2020Co-Authors: Konstantinos Koufos, Harpreet S. Dhillon, Mehrdad Dianati, Carl P DettmannAbstract:In this paper, we consider a Cox point Process driven by the Manhattan Poisson line Process. We calculate the exact cumulative distribution function (CDF) of the path distance (L1 norm) between a randomly selected intersection and the $k$-th nearest node of the Cox Process. The CDF is expressed as a sum over the integer partition function $p\!\left(k\right)$, which allows us to numerically evaluate the CDF in a simple manner for practical values of $k$. These distance distributions can be used to study the $k$-coverage of broadcast signals transmitted from a \ac{RSU} located at an intersection in intelligent transport systems (ITS). Also, they can be insightful for network dimensioning in vehicle-to-everything (V2X) systems, because they can yield the exact distribution of network load within a cell, provided that the \ac{RSU} is placed at an intersection. Finally, they can find useful applications in other branches of science like spatial databases, emergency response planning, and districting.
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poisson line Cox Process foundations and applications to vehicular networks
Synthesis Lectures on Learning Networks and Algorithms, 2020Co-Authors: Harpreet S. Dhillon, Vishnu Vardhan ChetlurAbstract:Abstract This book provides a comprehensive treatment of the Poisson line Cox Process (PLCP) and its applications to vehicular networks. The PLCP is constructed by placing points on each line of a ...
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poisson line Cox Process asymptotic characterization and performance analysis of vehicular networks
Global Communications Conference, 2019Co-Authors: Vishnu Vardhan Chetlur, Harpreet S. DhillonAbstract:In this paper, we consider a cellular vehicle-to-everything (C-V2X) network in which the road system is modeled by a Poisson line Process (PLP) and the locations of vehicular nodes and RSUs on each road are modeled by a 1D Poisson point Process (PPP), thereby forming a Poisson line Cox Process (PLCP). Further, we model the locations of cellular macro base stations (MBSs) by a 2D PPP. While the PLCP model has recently been used to characterize vehicular network performance, the technical complexity induced by the doubly stochastic nature of the PLCP has deterred the inclusion of shadowing effects in these studies. In this paper, we approach towards closing this knowledge gap by computing the signal-to-interference ratio (SIR)-based coverage probability of a typical receiver in this network under log-normal shadowing. In order to enable this analysis, we first establish that the PLCP asymptotically converges to a 2D PPP and using this result, we develop an approximate yet accurate spatial model that is much more conducive to the coverage analysis in the presence of shadowing than the PLCP. Our analysis offers useful insights into the deployment of RSUs based on their impact on the coverage performance of the network under various scenarios.
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Success Probability and Area Spectral Efficiency of a VANET Modeled as a Cox Process
arXiv: Information Theory, 2018Co-Authors: Vishnu Vardhan Chetlur, Harpreet S. DhillonAbstract:This paper analyzes the performance of a vehicular ad hoc network (VANET) modeled as a Cox Process, where the spatial layout of the roads is modeled by a Poisson line Process (PLP) and the locations of nodes on each line are modeled as a 1D Poisson point Process (PPP). For this setup, we characterize the success probability of a typical link and the area spectral efficiency (ASE) of the network assuming slotted ALOHA as the channel access scheme. We then concretely establish that the success probability of a typical link in a VANET modeled using a Cox Process converges to that of a 1D and 2D PPP for some extreme values of the line and node densities. We also study the trends in success probability as a function of the system parameters and show that the optimum transmission probability that maximizes the ASE for this Cox Process model differs significantly from those of the relatively-simpler 1D and 2D PPP models used commonly in the literature to model vehicular networks.
Jiwook Jang - One of the best experts on this subject based on the ideXlab platform.
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catastrophe insurance derivatives pricing using a Cox Process with jump diffusion cir intensity
International Journal of Theoretical and Applied Finance, 2018Co-Authors: Jiwook Jang, Jong Jun Park, Hyun Jin JangAbstract:We propose an analytical pricing method for stop-loss reinsurance contracts and catastrophe insurance derivatives using a Cox Process with jump diffusion Cox–Ingersoll–Ross (CIR) intensity. The exp...
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a risk model with renewal shot noise Cox Process
Insurance Mathematics & Economics, 2015Co-Authors: Angelos Dassios, Jiwook Jang, Hongbiao ZhaoAbstract:In this paper we generalise the risk models beyond the ordinary framework of affine Processes or Markov Processes and study a risk Process where the claim arrivals are driven by a Cox Process with renewal shot-noise intensity. The upper bounds of the finite-horizon and infinite-horizon ruin probabilities are investigated and an efficient and exact Monte Carlo simulation algorithm for this new Process is developed. A more efficient estimation method for the infinite-horizon ruin probability based on importance sampling via a suitable change of probability measure is also provided; illustrative numerical examples are also provided.
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a bivariate shot noise self exciting Process for insurance
Insurance Mathematics & Economics, 2013Co-Authors: Jiwook Jang, Angelos DassiosAbstract:In this paper, we study a bivariate shot noise self-exciting Process. This Process includes both externally excited joint jumps, which are distributed according to a shot noise Cox Process, and two separate self-excited jumps, which are distributed according to the branching structure of a Hawkes Process with an exponential fertility rate, respectively. A constant rate of exponential decay is included in this Process as it can play a role as the time value of money in economics, finance and insurance applications. We analyse this Process systematically for its theoretical distributional properties, based on the piecewise deterministic Markov Process theory developed by Davis (1984), and the martingale methodology used by Dassios and Jang (2003). The analytic expressions of the Laplace transforms of this Process and the moments are presented, which have the potential to be applicable to a variety of problems in economics, finance and insurance. In this paper, as an application of this Process, we provide insurance premium calculations based on its moments. Numerical examples show that this point Process can be used for the modelling of discounted aggregate losses from catastrophic events.
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measuring tail dependence for aggregate collateral losses using bivariate compound Cox Process with shot noise intensity
Social Science Research Network, 2010Co-Authors: Jiwook JangAbstract:A catastrophic event such as flood, storm, hail, bushfire and earthquake brings about damages in properties, motors and interruption of businesses collaterally. Also a couple of losses incurred collaterally from the World Trade Centre (WTC) catastrophe, Hurricane Katrina and Victorian Bushfire. However it has not been developed a suitable model for insurance companies either to measure tail dependence between these collateral losses or relevant risk measures that can be used as insurance risk premiums. The first aim of this paper is to measure tail dependence between collateral losses as insurance industry is more concerned with dependence between extreme losses. The second is to calculate conditional probabilities and conditional expectations as relevant risk measures. To achieve these aims, we use bivariate compound Process where a Cox Process with shot noise intensity is used to count collateral losses from catastrophic events. Homogeneous Poisson Process is also examined as its counterpart for the case where the catastrophic loss frequency rate is deterministic. Using a member of Farlie-Gumbel-Morgenstern copula with exponential margins, we derive explicit expressions of joint Laplace transforms of aggregate collateral losses. Fast Fourier transform is used to obtain the joint distributions of aggregate collateral losses, with which we calculate relevant risk measures. The figures of the joint distributions of collateral losses, their contours and numerical calculations of risk measures are provided.
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the distribution of the interval between events of a Cox Process with shot noise intensity
LSE Research Online Documents on Economics, 2008Co-Authors: Angelos Dassios, Jiwook JangAbstract:Applying piecewise deterministic Markov Processes theory, the probability generating function of a Cox Process, incorporating with shot noise Process as the claim intensity, is obtained. We also derive the Laplace transform of the distribution of the shot noise Process at claim jump times, using stationary assumption of the shot noise Process at any times. Based on this Laplace transform and from the probability generating function of a Cox Process with shot noise intensity, we obtain the distribution of the interval of a Cox Process with shot noise intensity for insurance claims and its moments, that is, mean and variance.
Vishnu Vardhan Chetlur - One of the best experts on this subject based on the ideXlab platform.
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shortest path distance in manhattan poisson line Cox Process
Journal of Statistical Physics, 2020Co-Authors: Vishnu Vardhan Chetlur, Harpreet S. Dhillon, Carl P DettmannAbstract:While the Euclidean distance characteristics of the Poisson line Cox Process (PLCP) have been investigated in the literature, the analytical characterization of the path distances is still an open problem. In this paper, we solve this problem for the stationary Manhattan Poisson line Cox Process (MPLCP), which is a variant of the PLCP. Specifically, we derive the exact cumulative distribution function (CDF) for the length of the shortest path to the nearest point of the MPLCP in the sense of path distance measured from two reference points: (i) the typical intersection of the Manhattan Poisson line Process (MPLP), and (ii) the typical point of the MPLCP. We also discuss the application of these results in infrastructure planning, wireless communication, and transportation networks.
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poisson line Cox Process foundations and applications to vehicular networks
Synthesis Lectures on Learning Networks and Algorithms, 2020Co-Authors: Harpreet S. Dhillon, Vishnu Vardhan ChetlurAbstract:Abstract This book provides a comprehensive treatment of the Poisson line Cox Process (PLCP) and its applications to vehicular networks. The PLCP is constructed by placing points on each line of a ...
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poisson line Cox Process asymptotic characterization and performance analysis of vehicular networks
Global Communications Conference, 2019Co-Authors: Vishnu Vardhan Chetlur, Harpreet S. DhillonAbstract:In this paper, we consider a cellular vehicle-to-everything (C-V2X) network in which the road system is modeled by a Poisson line Process (PLP) and the locations of vehicular nodes and RSUs on each road are modeled by a 1D Poisson point Process (PPP), thereby forming a Poisson line Cox Process (PLCP). Further, we model the locations of cellular macro base stations (MBSs) by a 2D PPP. While the PLCP model has recently been used to characterize vehicular network performance, the technical complexity induced by the doubly stochastic nature of the PLCP has deterred the inclusion of shadowing effects in these studies. In this paper, we approach towards closing this knowledge gap by computing the signal-to-interference ratio (SIR)-based coverage probability of a typical receiver in this network under log-normal shadowing. In order to enable this analysis, we first establish that the PLCP asymptotically converges to a 2D PPP and using this result, we develop an approximate yet accurate spatial model that is much more conducive to the coverage analysis in the presence of shadowing than the PLCP. Our analysis offers useful insights into the deployment of RSUs based on their impact on the coverage performance of the network under various scenarios.
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Success Probability and Area Spectral Efficiency of a VANET Modeled as a Cox Process
arXiv: Information Theory, 2018Co-Authors: Vishnu Vardhan Chetlur, Harpreet S. DhillonAbstract:This paper analyzes the performance of a vehicular ad hoc network (VANET) modeled as a Cox Process, where the spatial layout of the roads is modeled by a Poisson line Process (PLP) and the locations of nodes on each line are modeled as a 1D Poisson point Process (PPP). For this setup, we characterize the success probability of a typical link and the area spectral efficiency (ASE) of the network assuming slotted ALOHA as the channel access scheme. We then concretely establish that the success probability of a typical link in a VANET modeled using a Cox Process converges to that of a 1D and 2D PPP for some extreme values of the line and node densities. We also study the trends in success probability as a function of the system parameters and show that the optimum transmission probability that maximizes the ASE for this Cox Process model differs significantly from those of the relatively-simpler 1D and 2D PPP models used commonly in the literature to model vehicular networks.
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coverage analysis of a vehicular network modeled as Cox Process driven by poisson line Process
IEEE Transactions on Wireless Communications, 2018Co-Authors: Vishnu Vardhan Chetlur, Harpreet S. DhillonAbstract:In this paper, we consider a vehicular network in which the wireless nodes are located on a system of roads. We model the roadways, which are predominantly straight and randomly oriented, by a Poisson line Process (PLP) and the locations of nodes on each road as a homogeneous 1D Poisson point Process. Assuming that each node transmits independently, the locations of transmitting and receiving nodes are given by two Cox Processes driven by the same PLP. For this setup, we derive the coverage probability of a typical receiver, which is an arbitrarily chosen receiving node, assuming independent Nakagami- $m$ fading over all wireless channels. Assuming that the typical receiver connects to its closest transmitting node in the network, we first derive the distribution of the distance between the typical receiver and the serving node to characterize the desired signal power. We then characterize coverage probability for this setup, which involves two key technical challenges. First, we need to handle several cases as the serving node can possibly be located on any line in the network and the corresponding interference experienced at the typical receiver is different in each case. Second, conditioning on the serving node imposes constraints on the spatial configuration of lines, which requires careful analysis of the conditional distribution of the lines. We address these challenges in order to characterize the interference experienced at the typical receiver. We then derive an exact expression for coverage probability in terms of the derivative of Laplace transform of interference power distribution. We analyze the trends in coverage probability as a function of the network parameters: line density and node density. We also provide some theoretical insights by studying the asymptotic characteristics of coverage probability.
Angelos Dassios - One of the best experts on this subject based on the ideXlab platform.
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a risk model with renewal shot noise Cox Process
Insurance Mathematics & Economics, 2015Co-Authors: Angelos Dassios, Jiwook Jang, Hongbiao ZhaoAbstract:In this paper we generalise the risk models beyond the ordinary framework of affine Processes or Markov Processes and study a risk Process where the claim arrivals are driven by a Cox Process with renewal shot-noise intensity. The upper bounds of the finite-horizon and infinite-horizon ruin probabilities are investigated and an efficient and exact Monte Carlo simulation algorithm for this new Process is developed. A more efficient estimation method for the infinite-horizon ruin probability based on importance sampling via a suitable change of probability measure is also provided; illustrative numerical examples are also provided.
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a bivariate shot noise self exciting Process for insurance
Insurance Mathematics & Economics, 2013Co-Authors: Jiwook Jang, Angelos DassiosAbstract:In this paper, we study a bivariate shot noise self-exciting Process. This Process includes both externally excited joint jumps, which are distributed according to a shot noise Cox Process, and two separate self-excited jumps, which are distributed according to the branching structure of a Hawkes Process with an exponential fertility rate, respectively. A constant rate of exponential decay is included in this Process as it can play a role as the time value of money in economics, finance and insurance applications. We analyse this Process systematically for its theoretical distributional properties, based on the piecewise deterministic Markov Process theory developed by Davis (1984), and the martingale methodology used by Dassios and Jang (2003). The analytic expressions of the Laplace transforms of this Process and the moments are presented, which have the potential to be applicable to a variety of problems in economics, finance and insurance. In this paper, as an application of this Process, we provide insurance premium calculations based on its moments. Numerical examples show that this point Process can be used for the modelling of discounted aggregate losses from catastrophic events.
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a dynamic contagion Process
Advances in Applied Probability, 2011Co-Authors: Angelos Dassios, Hongbiao ZhaoAbstract:We introduce a new point Process, the dynamic contagion Process, by generalising the Hawkes Process and the Cox Process with shot noise intensity. Our Process includes both self-excited and externally excited jumps, which could be used to model the dynamic contagion impact from endogenous and exogenous factors of the underlying system. We have systematically analysed the theoretical distributional properties of this new Process, based on the piecewise-deterministic Markov Process theory developed in Davis (1984), and the extension of the martingale methodology used in Dassios and Jang (2003). The analytic expressions of the Laplace transform of the intensity Process and the probability generating function of the point Process have been derived. An explicit example of specified jumps with exponential distributions is also given. The object of this study is to produce a general mathematical framework for modelling the dependence structure of arriving events with dynamic contagion, which has the potential to be applicable to a variety of problems in economics, finance, and insurance. We provide an application of this Process to credit risk, and a simulation algorithm for further industrial implementation and statistical analysis.
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the distribution of the interval between events of a Cox Process with shot noise intensity
LSE Research Online Documents on Economics, 2008Co-Authors: Angelos Dassios, Jiwook JangAbstract:Applying piecewise deterministic Markov Processes theory, the probability generating function of a Cox Process, incorporating with shot noise Process as the claim intensity, is obtained. We also derive the Laplace transform of the distribution of the shot noise Process at claim jump times, using stationary assumption of the shot noise Process at any times. Based on this Laplace transform and from the probability generating function of a Cox Process with shot noise intensity, we obtain the distribution of the interval of a Cox Process with shot noise intensity for insurance claims and its moments, that is, mean and variance.
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kalman bucy filtering for linear systems driven by the Cox Process with shot noise intensity and its application to the pricing of reinsurance contracts
Journal of Applied Probability, 2005Co-Authors: Angelos Dassios, Jiwook JangAbstract:In practical situations, we observe the number of claims to an insurance portfolio but not the claim intensity. It is therefore of interest to try to solve the 'filtering problem'; that is, to obtain the best estimate of the claim intensity on the basis of reported claims. In order to use the Kalman-Bucy filter, based on the Cox Process incorporating a shot noise Process as claim intensity, we need to approximate it by a Gaussian Process. We demonstrate that, if the primary-event arrival rate of the shot noise Process is reasonably large, we can then approximate the intensity, claim arrival, and aggregate loss Processes by a three-dimensional Gaussian Process. We establish weak-convergence results. We then use the Kalman-Bucy filter and we obtain the price of reinsurance contracts involving high-frequency events.
Francois Bastardie - One of the best experts on this subject based on the ideXlab platform.
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a statistical model for estimation of fish density including correlation in size space time and between species from research survey data
PLOS ONE, 2014Co-Authors: Rasmus J Nielsen, Peter Lewy, Kasper Kristensen, Francois BastardieAbstract:Trawl survey data with high spatial and seasonal coverage were analysed using a variant of the Log Gaussian Cox Process (LGCP) statistical model to estimate unbiased relative fish densities. The model estimates correlations between observations according to time, space, and fish size and includes zero observations and over-dispersion. The model utilises the fact the correlation between numbers of fish caught increases when the distance in space and time between the fish decreases, and the correlation between size groups in a haul increases when the difference in size decreases. Here the model is extended in two ways. Instead of assuming a natural scale size correlation, the model is further developed to allow for a transformed length scale. Furthermore, in the present application, the spatial- and size-dependent correlation between species was included. For cod (Gadus morhua) and whiting (Merlangius merlangus), a common structured size correlation was fitted, and a separable structure between the time and space-size correlation was found for each species, whereas more complex structures were required to describe the correlation between species (and space-size). The within-species time correlation is strong, whereas the correlations between the species are weaker over time but strong within the year.
