scholarly journals Large deviation principle for empirical measures generated by Cox point processes

2003 ◽  
Vol 97 (1) ◽  
pp. 87-106
Author(s):  
Tomasz Schreiber
Keyword(s):  
Point Processes ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Empirical Measures ◽  
Deviation Principle

Large deviation principles for connectable receivers in wireless networks

2016 ◽  
Vol 48 (4) ◽  
pp. 1061-1094 ◽  
Author(s):  
Christian Hirsch ◽  
Benedikt Jahnel ◽  
Paul Keeler ◽  
Robert I. A. Patterson
Keyword(s):  
Wireless Networks ◽  
Importance Sampling ◽  
Point Processes ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Empirical Measure ◽  
Deviation Principle ◽  
Large Deviation Principles ◽  
Sampling Algorithms ◽  
Connectivity Threshold

AbstractWe study large deviation principles for a model of wireless networks consisting of Poisson point processes of transmitters and receivers. To each transmitter we associate a family of connectable receivers whose signal-to-interference-and-noise ratio is larger than a certain connectivity threshold. First, we show a large deviation principle for the empirical measure of connectable receivers associated with transmitters in large boxes. Second, making use of the observation that the receivers connectable to the origin form a Cox point process, we derive a large deviation principle for the rescaled process of these receivers as the connection threshold tends to 0. Finally, we show how these results can be used to develop importance sampling algorithms that substantially reduce the variance for the estimation of probabilities of certain rare events such as users being unable to connect.

Large deviation principle for the field in prequantum classical statistical field theory

2017 ◽  
Vol 20 (04) ◽  
pp. 1750025
Author(s):  
Andrei Khrennikov ◽  
Achref Majid
Keyword(s):  
Field Theory ◽  
Random Field ◽  
Field Model ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Background Field ◽  
Deviation Principle ◽  
Statistical Field ◽  
Statistical Field Theory

In this paper, we prove a large deviation principle for the background field in prequantum statistical field model. We show a number of examples by choosing a specific random field in our model.

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