Second-Order Efficient Test for Inhomogeneous Poisson Processes

2007 ◽  
Vol 10 (2) ◽  
pp. 181-208 ◽  
Author(s):  
Fazli Kh
Keyword(s):  
Second Order ◽  
Poisson Processes ◽  
Efficient Test ◽  
Inhomogeneous Poisson Processes

Random Johnson-Mehl tessellations

1992 ◽  
Vol 24 (04) ◽  
pp. 814-844 ◽  
Author(s):  
Jesper Møller
Keyword(s):  
Euclidean Space ◽  
Second Order ◽  
Poisson Processes ◽  
Dimensional Euclidean Space ◽  
Inhomogeneous Poisson Processes

A unified exposition of random Johnson–Mehl tessellations in d-dimensional Euclidean space is presented. In particular, Johnson-Mehl tessellations generated by time-inhomogeneous Poisson processes and nucleation-exclusion models are studied. The ‘practical' cases d = 2 and d = 3 are discussed in detail. Several new results are established, including first- and second-order moments of various characteristics for both Johnson–Mehl tesselations and sectional Johnson–Mehl tessellations.

Random Johnson-Mehl tessellations

1992 ◽  
Vol 24 (4) ◽  
pp. 814-844 ◽  
Author(s):  
Jesper Møller
Keyword(s):  
Euclidean Space ◽  
Second Order ◽  
Poisson Processes ◽  
Dimensional Euclidean Space ◽  
Inhomogeneous Poisson Processes

A unified exposition of random Johnson–Mehl tessellations in d-dimensional Euclidean space is presented. In particular, Johnson-Mehl tessellations generated by time-inhomogeneous Poisson processes and nucleation-exclusion models are studied. The ‘practical' cases d = 2 and d = 3 are discussed in detail. Several new results are established, including first- and second-order moments of various characteristics for both Johnson–Mehl tesselations and sectional Johnson–Mehl tessellations.

Generation of Johnson-Mehl crystals and comparative analysis of models for random nucleation

1995 ◽  
Vol 27 (02) ◽  
pp. 367-383 ◽  
Author(s):  
Jesper Møller
Keyword(s):  
Comparative Analysis ◽  
Poisson Processes ◽  
Three Dimensions ◽  
Empirical Results ◽  
Random Nucleation ◽  
Inhomogeneous Poisson Processes

Simulation procedures for typical Johnson-Mehl crystals generated under various models for random nucleation are proposed. These procedures include algorithms for simulating spatio-time-inhomogeneous Poisson processes. Empirical results for a particular class of Johnson-Mehl tessellations in two and three dimensions show remarkably different crystals.

scholarly journals A fluid limit for a cache algorithm with general request processes

2010 ◽  
Vol 42 (03) ◽  
pp. 816-833 ◽  
Author(s):  
Takayuki Osogami
Keyword(s):  
Stochastic Models ◽  
Point Processes ◽  
Original System ◽  
Poisson Processes ◽  
Fluid Limit ◽  
Average Probability ◽  
Inhomogeneous Poisson Processes ◽  
Formal Limit ◽  
Stochastic Point Processes ◽  
General Stochastic

We introduce a formal limit, which we refer to as a fluid limit, of scaled stochastic models for a cache managed with the least-recently-used algorithm when requests are issued according to general stochastic point processes. We define our fluid limit as a superposition of dependent replications of the original system with smaller item sizes when the number of replications approaches ∞. We derive the average probability that a requested item is not in a cache (average miss probability) in the fluid limit. We show that, when requests follow inhomogeneous Poisson processes, the average miss probability in the fluid limit closely approximates that in the original system. Also, we compare the asymptotic characteristics, as the cache size approaches ∞, of the average miss probability in the fluid limit to those in the original system.

ON THE IDENTIFICATION OF THE SOURCE OF EMISSION ON THE PLANE

2019 ◽  
Vol 53 (2 (249)) ◽  
pp. 75-81
Author(s):  
N.V. Arakelyan ◽  
Yu.A. Kutoyants
Keyword(s):  
Asymptotic Properties ◽  
Radioactive Source ◽  
Poisson Processes ◽  
Inhomogeneous Poisson Processes ◽  
The Moment ◽  
Source Emission

We consider the problem of identification of the position and the moment of the beginning of a radioactive source emission on the plane. The acts of emission constitute inhomogeneous Poisson processes and are registered by $ K $ detectors on the plane. We suppose that the moments of arriving of the signals at the detectors are measured with some small errors. Then, using these estimate, we construct the estimators of the position of source and the moment of the beginning of emission. We study the asymptotic properties of these estimators for large signals and prove their consistency.

scholarly journals A fluid limit for a cache algorithm with general request processes

2010 ◽  
Vol 42 (3) ◽  
pp. 816-833 ◽  
Author(s):  
Takayuki Osogami
Keyword(s):  
Stochastic Models ◽  
Point Processes ◽  
Original System ◽  
Poisson Processes ◽  
Fluid Limit ◽  
Average Probability ◽  
Inhomogeneous Poisson Processes ◽  
Formal Limit ◽  
Stochastic Point Processes ◽  
General Stochastic

We introduce a formal limit, which we refer to as a fluid limit, of scaled stochastic models for a cache managed with the least-recently-used algorithm when requests are issued according to general stochastic point processes. We define our fluid limit as a superposition of dependent replications of the original system with smaller item sizes when the number of replications approaches ∞. We derive the average probability that a requested item is not in a cache (average miss probability) in the fluid limit. We show that, when requests follow inhomogeneous Poisson processes, the average miss probability in the fluid limit closely approximates that in the original system. Also, we compare the asymptotic characteristics, as the cache size approaches ∞, of the average miss probability in the fluid limit to those in the original system.

Weak homogenization of point processes by space deformations

2000 ◽  
Vol 32 (4) ◽  
pp. 948-959 ◽  
Author(s):  
R. Senoussi ◽  
J. Chadœuf ◽  
D. Allard
Keyword(s):  
Point Process ◽  
Stationary Point ◽  
Point Processes ◽  
Second Order ◽  
Poisson Processes ◽  
Borel Set ◽  
First Order ◽  
Stationary Point Process

We study the transformation of a non-stationary point process ξ on ℝn into a weakly stationary point process ͂ξ, with ͂ξ(B) = ξ(Φ-1(B)), where B is a Borel set, via a deformation Φ of the space ℝn. When the second-order measure is regular, Φ is uniquely determined by the homogenization equations of the second-order measure. In contrast, the first-order homogenization transformation is not unique. Several examples of point processes and transformations are investigated with a particular interest to Poisson processes.

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