Search results for "Poisson process"
showing 10 items of 23 documents
Segmentation algorithm for non-stationary compound Poisson processes
2010
We introduce an algorithm for the segmentation of a class of regime switching processes. The segmentation algorithm is a non parametric statistical method able to identify the regimes (patches) of a time series. The process is composed of consecutive patches of variable length. In each patch the process is described by a stationary compound Poisson process, i.e. a Poisson process where each count is associated with a fluctuating signal. The parameters of the process are different in each patch and therefore the time series is non-stationary. Our method is a generalization of the algorithm introduced by Bernaola-Galván, et al. [Phys. Rev. Lett. 87, 168105 (2001)]. We show that the new algori…
Predator population depending on lemming cycles
2016
In this paper, a Langevin equation for predator population with multiplicative correlated noise is analyzed. The noise source, which is a nonnegative random pulse noise with regulated periodicity, corresponds to the prey population cycling. The increase of periodicity of noise affects the average predator density at the stationary state.
Hitting straight lines by compound Poisson process paths
1990
In a recent article Mallows and Nair (1989,Ann. Inst. Statist. Math.,41, 1–8) determined the probability of intersectionP{X(t)=αt for somet≥0} between a compound Poisson process {X(t), t≥0} and a straight line through the origin. Using four different approaches (direct probabilistic, via differential equations and via Laplace transforms) we extend their results to obtain the probability of intersection between {X(t), t≥0} and arbitrary lines. Also, we display a relationship with the theory of Galton-Watson processes. Additional results concern the intersections with two (or more) parallel lines.
Estimating Mean Lifetime from Partially Observed Events in Nuclear Physics
2022
Abstract The mean lifetime is an important characteristic of particles to be identified in nuclear physics. State-of-the-art particle detectors can identify the arrivals of single radioactive nuclei as well as their subsequent radioactive decays (departures). Challenges arise when the arrivals and departures are unmatched and the departures are only partially observed. An inefficient solution is to run experiments where the arrival rate is set very low to allow for the matching of arrivals and departures. We propose an estimation method that works for a wide range of arrival rates. The method combines an initial estimator and a numerical bias correction technique. Simulations and examples b…
Erratum to “Simulation of BSDEs with jumps by Wiener Chaos expansion” [Stochastic Process. Appl. 126 (2016) 2123–2162]
2017
Abstract We correct Proposition 2.9 from “Simulation of BSDEs with jumps by Wiener Chaos expansion” published in Stochastic Processes and their Applications, 126 (2016) 2123–2162. The proposition which provides an expression for the expectation of products of multiple integrals (w.r.t. Brownian motion and compensated Poisson process) requires a stronger integrability assumption on the kernels than previously stated. This does not affect the remaining results of the article.
Hard-Core Thinnings of Germ‒Grain Models with Power-Law Grain Sizes
2013
Random sets with long-range dependence can be generated using a Boolean model with power-law grain sizes. We study thinnings of such Boolean models which have the hard-core property that no grains overlap in the resulting germ‒grain model. A fundamental question is whether long-range dependence is preserved under such thinnings. To answer this question, we study four natural thinnings of a Poisson germ‒grain model where the grains are spheres with a regularly varying size distribution. We show that a thinning which favors large grains preserves the slow correlation decay of the original model, whereas a thinning which favors small grains does not. Our most interesting finding concerns the c…
A note on Malliavin smoothness on the Lévy space
2017
We consider Malliavin calculus based on the Itô chaos decomposition of square integrable random variables on the Lévy space. We show that when a random variable satisfies a certain measurability condition, its differentiability and fractional differentiability can be determined by weighted Lebesgue spaces. The measurability condition is satisfied for all random variables if the underlying Lévy process is a compound Poisson process on a finite time interval. peerReviewed
A simplified analysis for the evaluation of stochastic response of elasto-plastic oscillators
1999
Abstract The paper deals with dynamic hysteretic oscillators without post-yielding hardening, called ideal elasto-plastic oscillators, subjected to white noise. They are characterized by the fact that they do not reach stationarity even though excited by stationary stochastic processes. A simplified solution procedure to capture this behaviour is presented in this paper. It is based on modelling the accumulated plastic deformations as a homogeneous compound Poisson process. In particular, two aspects are addressed in the paper: (1) evaluation of the probabilistic parameters of the accumulated plastic deformation process; and (2) evaluation of the second-order cumulants of the response by me…
Stochastic modeling and prediction of catalytic converters degradation
2009
This paper proposes a stochastic model for describing the degradation process of catalytic converters over time, where the degradation is indirectly measured through the emission of complex hydrocarbons (HC) in legislated driving cycles. The proposed model is the superposition of two processes, the former being a dependent increments process which describes the actual degradation process, and the latter a white noise process which models the experimental errors. In particular, the proposed model assumes that the degradation growth in a small usage interval depends on the degradation level at the beginning of the interval, rather than on the age of the converter. The model has been applied t…
Hysteretic Systems Subjected to Delta Correlated Input
1994
The paper deals with the evaluation of the probabilistic response of a single degree of freedom elastic-perfectly plastic system subjected to a delta correlated input process. The probabilistic characterisation of the response is here obtained by considering the accumulated plastic deformations as a compound homogeneous Poisson process independent of the external input. In this case the former can be considered as an external noise acting on the linear system. A closed form solution is also obtained and the analytic expression is compared with the customary Monte-Carlo method.