Poisson Process
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Recent papers in Poisson Process
We discuss the close link between intermittent events ('quakes') and extremal noise fluctuations which has been advocated in recent numerical and theoretical work. From the idea that record-breaking noise fluctuations trigger the quakes,... more
Hard-core Strauss disc processes with inhibition distance r and disc radius R are considered. The points in the Strauss point process are thought of as trees and the discs as crowns. Formulas for the mean and the variance of the vacancy... more
Databases and online systems have dramatically changed the way businesses transact and maintain records. The database-supported transaction systems enable businesses to conduct their businesses electronically, leading to quicker exchange... more
We consider a Poisson process that is modulated in such a way that the arrival rate at any time depends on the state of a semi-Markov process. This presents an interesting generalization of Poisson processes with important implications in... more
Consider a stochastic process (X; A), where X represents the evolution of a system over time, and A is an associated point process that has stationary independent increments. Suppose we are interested in estimating the time average... more
A stochastic entirely mechanistic model of metastatic progression of cancer is developed. Based on this model the joint conditional distribution of the ordered sizes of detectable metastases given their number, n, is computed. It is shown... more
The belief that neurones transmit information in the form of a firing rate code is almost universal. However, we argue that at least in some situations, the efficiency of a coding strategy based on rate coding is surprisingly poor. A... more
In combinatorics and analysis of algorithms a Poisson version of a problem (henceforth called Poisson model or poissonization) is often easier to solve than the original one, which we name here the Bernoulli model. Poissonization is a... more
The European Union has been promoting an homogenisation of the design rules for earthquake resistant structures through the Eurocode 8, which will soon become the official standard (CEN, 2003). However, the zonation for the basic... more
The integrate-and-fire neuron model describes the state of a neuron in terms of its membrane potential, which is determined by the synaptic inputs and the injected current that the neuron receives. When the membrane potential reaches a... more
In studies of recurrent events, such as epileptic seizures, there can be a large amount of information about a cohort over a period of time, but current methods for these data are often unable to utilize all of the available information.... more
We propose a framework for studying optimal market making policies in a limit order book (LOB). The bid-ask spread of the LOB is modelled by a Markov chain with finite values, multiple of the tick size, and subordinated by the Poisson... more
In this paper a fractal analysis study of VoIP traffic is presented. The characteristics of measured VoIP traffic on both call and packet level have been investigated. The results support the popular Poisson process for VoIP call arrival... more
Distribution of some statistics, especially rank based, with censored data are hard to get. Even if they can be worked out for small samples, they are likely to be prohibitively expensive for larger sample sizes. Therefore we need to work... more
Schrödinger's equation and the heat equation are connected to one another by analytic continuation, as are the Feynman integral and the Wiener integral. We extend this form of correspondence to the relativistic domain by... more
CAÑELLAS, B.; ORFILA, A.; MÉNDEZ, F.J.; MENÉNDEZ, M. and TINTORÉ, J., 2007. Application of a POT model to estimate the extreme significant wave height levels around the Extreme value wave climate analysis at a particular site requires... more
We propose a new discrete-time model of returns in which jumps capture persistence in the conditional variance and higher-order moments. Jump arrival is governed by a heterogeneous Poisson process. The intensity is directed by a latent... more
We consider the pricing of options when delta hedging only takes place at discrete intervals. We show how to include transaction costs, jumps and stochastic volatility while optimally, but discretely, dynamically hedging. Copyright © 2009... more
We propose a new discrete-time model of returns in which jumps capture persistence in the conditional variance and higher-order moments. Jump arrival is governed by a heterogeneous Poisson process. The intensity is directed by a latent... more
Traditional tool life models do not take into account the variation inherent in metal cutting processes. As a consequence, the real tool life rarely matches the predicted values. To compensate for this uncertainty, tools are usually... more
This paper is intended as a guide to building insurance risk (loss) models. A typical model for insurance risk, the so-called collective risk model, treats the aggregate loss as having a compound distribution with two main components: one... more
Information about delays can enhance service quality in many industries. Delay information can take many forms, with different degrees of precision. Different levels of information have different effects on customers and so on the overall... more
We describe a range of methods for the description and analysis of spatial point patterns in plant ecology. The conceptual basis of the methods is presented, and specific tests are compared, with the goal of providing guidelines... more
Abstrut-A large number of terminals transmitting data packets over a common radio channel to a central base station is studied. In inhibit sense multiple access (ISMA), the base station broadcasts a busy signal when an incoming packet is... more
Purpose This paper aims to focus on the problem of the optimal relocation policy for a firm that faces two types of uncertainty: one about the moments in which new (and more efficient) sites will become available; and the other... more
In this paper we demonstrate how to use the importance sampling method to simulate rare events in a germ-grain model. We analyze conditions under which two germ-grain models are mutually absolutely continuous. We also find the likelihood... more
Motivated by the work of Segal and Segal on the Black-Scholes pricing formula in the quantum context, we study a quantum extension of the Black-Scholes equation within the context of Hudson-Parthasarathy quantum stochastic calculus. Our... more
The most recent financial crisis unveiled that liquidity risk is far more important and intricate than regulation have conceived. The shift from bank-based to market-based financial systems and from Deferred Net Systems to... more
The integrate-and-fire neuron model is one of the most widely used models for analyzing the behavior of neural systems. It describes the membrane potential of a neuron in terms of the synaptic inputs and the injected current that it... more
Let P be a Poisson process of intensity one in the infinite plane R 2 . We surround each point x of P by the open disc of radius r centred at x. Now let S n be a fixed disc of area n, and let C r (S n ) be the set of discs which intersect... more
We discuss some applications of the Mittag-Leffler function and related probability distributions in the theory of renewal processes and continuous time random walks. In particular we show the asymptotic (long time) equivalence of a... more
This paper presents an application of stochastic Petri nets (SPN) to calculate the availability of safety critical on-demand systems. Traditional methods of estimating system reliability include standards-based or field return-based... more
We base a theory of timing on the observation that signals of reinforcement elicit adjunctive behaviors. The transitions between these behaviors are well described as a Poisson process, with a rate constant proportional to the rate of... more
An incomplete market driven by a pair of Wiener and Poisson processes is considered. The range of European and American claim prices is determined.
In combinatorics and analysis of algorithms a Poisson version of a problem (henceforth called Poisson model or poissonization) is often easier to solve than the original one, which we name here the Bernoulli model. Poissonization is a... more
Consider a number of parallel queues, each with an arbitrary capacity and multiple identical exponential servers. The service discipline in each queue is firstcome-first-served (FCFS). Customers arrive according to a state-dependent... more
We present a novel statistical framework for detecting pre-determined shape classes in 2D cluttered point clouds, which are in turn extracted from images. In this modelbased approach, we use a 1D Poisson process for sampling points on... more
Various physiologic and biochemical shifts can follow meditation. Meditation has been implicated in impacting free radical activity. Ultraweak photon emission (UPE, biophoton emission) is a constituent of the metabolic processes in a... more
The Poisson-Voronoi map is a natural random planar map. Being planar, a specific instance can always be colored with 4 colors with adjacent cells having distinct colors. The question we consider here is whether such a coloring can be... more
We introduce here the Earthquake Network project which implements a world-wide smartphone-based sensor network for the detection of earthquakes. Thanks to the accelerometric sensor, smartphones possibly detect the waves of a quake and... more
The two parameter Poisson-Dirichlet distribution $PD(\alpha,\theta)$ is the distribution of an infinite dimensional random discrete probability. It is a generalization of Kingman's Poisson-Dirichlet distribution. The two parameter... more
In this paper we present an online approach for joint detection and tracking for multiple targets using variable rate particle filters (VRPFs). Unlike conventional models and particle filters, the proposed method utilises the applied... more
Shot-noise and fractional Poisson processes are instances of filtered Poisson processes. We here prove Girsanov theorem for this kind of processes and give an application to an estimate problem.