scholarly journals Asymptotic analysis of Poisson shot noise processes, and applications

2021 ◽  
Author(s):  
Giovanni Luca Torrisi ◽  
Emilio Leonardi
Keyword(s):  
Asymptotic Analysis ◽  
Shot Noise ◽  
Poisson Shot Noise

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

scholarly journals On fixed points of Poisson shot noise transforms

2002 ◽  
Vol 34 (04) ◽  
pp. 798-825 ◽  
Author(s):  
Aleksander M. Iksanov ◽  
Zbigniew J. Jurek
Keyword(s):  
Fixed Points ◽  
Power Function ◽  
Shot Noise ◽  
Response Functions ◽  
Tail Behavior ◽  
Absolutely Continuous ◽  
Exponential Moments ◽  
Poisson Shot Noise

Distributional fixed points of a Poisson shot noise transform (for nonnegative and nonincreasing response functions bounded by 1) are characterized. The tail behavior of fixed points is described. Typically they have either exponential moments or their tails are proportional to a power function, with exponent greater than −1. The uniqueness of fixed points is also discussed. Finally, it is proved that in most cases fixed points are absolutely continuous, apart from the possible atom at zero.

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 An insensitivity property of Lundberg's estimate for delayed claims

2000 ◽  
Vol 37 (03) ◽  
pp. 914-917 ◽  
Author(s):  
Pierre Brémaud
Keyword(s):  
Shot Noise ◽  
Life Insurance ◽  
Upper Bound ◽  
Short Note ◽  
Compound Poisson ◽  
Cramér’S Condition ◽  
Total Claim ◽  
Poisson Shot Noise ◽  
Ruin Problem

This short note shows that the Lundberg exponential upper bound in the ruin problem of non-life insurance with compound Poisson claims is also valid for the Poisson shot noise delayed-claims model, and that the optimal exponent depends only on the distribution of the total claim per accident, not on the time it takes to honour the claim. This result holds under Cramer's condition.

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