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Shot noise displaying simultaneously the Noah and Joseph effects.

Iddo Eliazar¹, Joseph Klafter

¹Department of Technology Management, Holon Institute of Technology, Holon 58102, Israel. eliazar@post.tau.ac.il

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|May 16, 2007

Summary

Shot noise processes with infinite variance, exhibiting the Noah effect, pose measurement challenges. A new Poisson-based analysis, using a Poissonian autocovariance function, quantifies both Noah and Joseph effects in these complex processes.

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Area of Science:

Stochastic processes
Signal processing
Statistical physics

Background:

Shot noise processes can exhibit infinite variance (Noah effect).
Standard autocovariance functions are undefined for infinite variance processes, hindering correlation analysis.
Simultaneous Noah and Joseph effects complicate process characterization.

Purpose of the Study:

To develop a novel analytical method for shot noise processes with infinite variance.
To enable the measurement of correlation structure in processes displaying the Noah effect.
To provide a quantitative analysis of shot noise processes exhibiting both Noah and Joseph effects.

Main Methods:

Development of a Poisson-based analysis framework.
Introduction of a Poissonian autocovariance function.
Application of the Poissonian methodology to quantify stationary and correlation structures.

Main Results:

The Poissonian autocovariance function is defined for shot noise processes with infinite variance.
This function accurately characterizes the stationary (amplitude) and correlation (temporal) behaviors.
The Poissonian methodology successfully quantifies processes with simultaneous Noah and Joseph effects.

Conclusions:

A robust method is established for analyzing complex shot noise processes.
The Poissonian approach overcomes limitations of traditional autocovariance functions.
Precise quantitative analysis of shot noise with infinite variance is now achievable.