Nonlinear Shot Noise: From aggregate dynamics to maximal dynamicsI. Eliazar1, 2 and J. Klafter2
1 Department of Technology Management, Holon Institute of Technology - Holon 58102, Israel
2 School of Chemistry, Sackler Faculty of Exact Sciences, Tel Aviv University - Tel Aviv 69978, Israel
received 1 January 2007; accepted in final form 3 April 2007; published May 2007
published online 3 May 2007
We consider Nonlinear Shot Noise systems in which external shots hit the system following an arbitrary Poissonian inflow and, after impact, dissipate to zero governed by an arbitrary nonlinear decay mechanism. The "standard" Shot Noise process tracks the shots aggregate (at any given time) and is non-Markov. In this letter we shift from aggregate dynamics to maximal dynamics -tracking the magnitude of the largest shot present in the system (at any given time). This yields a class of stochastic processes which: i) display a wide spectrum of random decay-surge evolutionary patterns; ii) are intrinsically nonlinear in both their decay and surge mechanisms; but yet, iii) turn out to be Markovian and analytically tractable. A detailed quantitative statistical analysis of this class of processes is presented.
05.40.Ca - Noise .
02.50.-r - Probability theory, stochastic processes, and statistics .
02.50.Ga - Markov processes.
© Europhysics Letters Association 2007