Large deviations of Poisson shot noise processes under heavy tail semi-exponential conditions

2010 ◽  
Vol 80 (15-16) ◽  
pp. 1200-1209 ◽  
Author(s):  
Gabriele Stabile ◽  
Giovanni Luca Torrisi
Keyword(s):  
Large Deviations ◽  
Shot Noise ◽  
Heavy Tail ◽  
Poisson Shot Noise

scholarly journals Large deviations for multidimensional state-dependent shot-noise processes

2015 ◽  
Vol 52 (04) ◽  
pp. 1097-1114 ◽  
Author(s):  
Amarjit Budhiraja ◽  
Pierre Nyquist
Keyword(s):  
Large Deviations ◽  
Shot Noise ◽  
Large Deviation ◽  
Physical Systems ◽  
Sample Paths ◽  
State Dependent ◽  
Light Tails ◽  
Engineering Sciences ◽  
Weak Convergence Approach ◽  
Poisson Shot Noise

Shot-noise processes are used in applied probability to model a variety of physical systems in, for example, teletraffic theory, insurance and risk theory, and in the engineering sciences. In this paper we prove a large deviation principle for the sample-paths of a general class of multidimensional state-dependent Poisson shot-noise processes. The result covers previously known large deviation results for one-dimensional state-independent shot-noise processes with light tails. We use the weak convergence approach to large deviations, which reduces the proof to establishing the appropriate convergence of certain controlled versions of the original processes together with relevant results on existence and uniqueness.

scholarly journals Sample Path Large Deviations of Poisson Shot Noise with Heavy-Tailed Semiexponential Distributions

2011 ◽  
Vol 48 (03) ◽  
pp. 688-698 ◽  
Author(s):  
Ken R. Duffy ◽  
Giovanni Luca Torrisi
Keyword(s):  
Large Deviations ◽  
Shot Noise ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Sample Path ◽  
Rate Function ◽  
Sample Paths ◽  
Heavy Tailed ◽  
Poisson Shot Noise ◽  
Sample Path Large Deviations

It is shown that the sample paths of Poisson shot noise with heavy-tailed semiexponential distributions satisfy a large deviation principle with a rate function that is insensitive to the shot shape. This demonstrates that, on the scale of large deviations, paths to rare events do not depend on the shot shape.

scholarly journals Sample Path Large Deviations of Poisson Shot Noise with Heavy-Tailed Semiexponential Distributions

2011 ◽  
Vol 48 (3) ◽  
pp. 688-698
Author(s):  
Ken R. Duffy ◽  
Giovanni Luca Torrisi
Keyword(s):  
Large Deviations ◽  
Shot Noise ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Sample Path ◽  
Rate Function ◽  
Sample Paths ◽  
Heavy Tailed ◽  
Poisson Shot Noise ◽  
Sample Path Large Deviations

It is shown that the sample paths of Poisson shot noise with heavy-tailed semiexponential distributions satisfy a large deviation principle with a rate function that is insensitive to the shot shape. This demonstrates that, on the scale of large deviations, paths to rare events do not depend on the shot shape.

scholarly journals Large deviations for multidimensional state-dependent shot-noise processes

2015 ◽  
Vol 52 (4) ◽  
pp. 1097-1114 ◽  
Author(s):  
Amarjit Budhiraja ◽  
Pierre Nyquist
Keyword(s):  
Large Deviations ◽  
Shot Noise ◽  
Large Deviation ◽  
Physical Systems ◽  
Sample Paths ◽  
State Dependent ◽  
Light Tails ◽  
Engineering Sciences ◽  
Weak Convergence Approach ◽  
Poisson Shot Noise

Shot-noise processes are used in applied probability to model a variety of physical systems in, for example, teletraffic theory, insurance and risk theory, and in the engineering sciences. In this paper we prove a large deviation principle for the sample-paths of a general class of multidimensional state-dependent Poisson shot-noise processes. The result covers previously known large deviation results for one-dimensional state-independent shot-noise processes with light tails. We use the weak convergence approach to large deviations, which reduces the proof to establishing the appropriate convergence of certain controlled versions of the original processes together with relevant results on existence and uniqueness.

Estimation variance of dual-rotating-retarder Mueller matrix polarimeter in the presence of Gaussian thermal noise and poisson shot noise

2019 ◽  
Vol 22 (2) ◽  
pp. 025701 ◽  
Author(s):  
Naicheng Quan ◽  
Chunmin Zhang ◽  
Tingkui Mu ◽  
Siyuan Li ◽  
Caiyin You
Keyword(s):  
Shot Noise ◽  
Thermal Noise ◽  
Mueller Matrix ◽  
Estimation Variance ◽  
Poisson Shot Noise
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