Correction to: Exponential Moments for Planar Tessellations

We consider a queue where the server is the Euclidean space, and the customers are random closed sets (RACSs) of the Euclidean space. These RACSs arrive according to a Poisson rain and each of them has a random service time (in the case of hail falling on the Euclidean plane, this is the height of the hailstone, whereas the RACS is its footprint). The Euclidean space serves customers at speed 1. The service discipline is a hard exclusion rule: no two intersecting RACSs can be served simultaneously and service is in the first-in–first-out order, i.e. only the hailstones in contact with the ground melt at speed 1, whereas the others are queued. A tagged RACS waits until all RACSs that arrived before it and intersecting it have fully melted before starting its own melting. We give the evolution equations for this queue. We prove that it is stable for a sufficiently small arrival intensity, provided that the typical diameter of the RACS and the typical service time have finite exponential moments. We also discuss the percolation properties of the stationary regime of the RACS in the queue.

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Vehicle License-plate Recognition Based on Exponential Moments

Revista Tecnica De La Facultad De Ingenieria Universidad Del Zulia ◽

10.21311/001.39.11.08 ◽

2017 ◽

Keyword(s):

License Plate ◽

License Plate Recognition ◽

Exponential Moments ◽

Vehicle License Plate Recognition

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Exponential Moments of Solutions for Nonlinear Equations with Catalytic Noise and Large Deviation

Recent Developments in Infinite-Dimensional Analysis and Quantum Probability ◽

10.1007/978-94-010-0842-6_6 ◽

2001 ◽

pp. 101-117

Author(s):

Isamu Dôku

Keyword(s):

Nonlinear Equations ◽

Large Deviation ◽

Exponential Moments

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Scan statistics of Lévy noises and marked empirical processes

Advances in Applied Probability ◽

10.1017/s0001867800003128 ◽

2009 ◽

Vol 41 (01) ◽

pp. 13-37 ◽

Cited By ~ 1

Author(s):

Zakhar Kabluchko ◽

Evgeny Spodarev

Keyword(s):

Random Variables ◽

Gumbel Distribution ◽

Empirical Processes ◽

Unit Cube ◽

Scan Statistics ◽

Lévy Noise ◽

Scan Statistic ◽

Exponential Moments ◽

Nonzero Probability ◽

Independent And Identically Distributed

Let n points be chosen independently and uniformly in the unit cube [0,1] d , and suppose that each point is supplied with a mark, the marks being independent and identically distributed random variables independent of the location of the points. To each cube R contained in [0,1] d we associate its score defined as the sum of marks of all points contained in R. The scan statistic is defined as the maximum of taken over all cubes R contained in [0,1] d . We show that if the marks are nonlattice random variables with finite exponential moments, having negative mean and assuming positive values with nonzero probability, then the appropriately normalized distribution of the scan statistic converges as n → ∞ to the Gumbel distribution. We also prove a corresponding result for the scan statistic of a Lévy noise with negative mean. The more elementary cases of zero and positive mean are also considered.

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