The maximal process of nonlinear shot noise

Iddo Eliazar and Joseph Klafter

Physica A: Statistical Mechanics and its Applications, 2009, vol. 388, issue 9, 1755-1779

Abstract: In the nonlinear shot noise system-model shots’ statistics are governed by general Poisson processes, and shots’ decay-dynamics are governed by general nonlinear differential equations. In this research we consider a nonlinear shot noise system and explore the process tracking, along time, the system’s maximal shot magnitude. This ‘maximal process’ is a stationary Markov process following a decay–surge evolution; it is highly robust, and it is capable of displaying both a wide spectrum of statistical behaviors and a rich variety of random decay–surge sample-path trajectories. A comprehensive analysis of the maximal process is conducted, including its Markovian structure, its decay–surge structure, and its correlation structure. All results are obtained analytically and in closed-form.

Keywords: Nonlinear shot noise; Maximal process; Decay–surge evolution; Growth–collapse evolution; PASTA (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:388:y:2009:i:9:p:1755-1779

DOI: 10.1016/j.physa.2009.01.010

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