We explore the behavior of power-law shot noise, for which the associated impulse response functions assume a decaying power-law form. We obtain expressions for the moments, moment generating functions, amplitude probability density functions, autocorrelation functions, and power spectral densities for a variety of parameters of the process. For certain parameters the power spectral density exhibits 1=f-type behavior over a substantial range of frequencies, so that the process serves as a source of 1=f ff shot noise for ff in the range 0 ! ff ! 2. For other parameters the amplitude probability density function is a L'evy-stable random variable with dimension less than unity. This process then behaves as a fractal shot noise that does not converge to a Gaussian amplitude distribution as the driving rate increases without limit. Fractal shot noise is a stationary continuous-time process that is fundamentally different from fractional Brownian motion. We consider several physical processes that are well described by power-law shot noise in certain domains: 1=f shot noise, Cherenkov radiation from a random stream of charged particles, diffusion of randomly injected concentration packets, the electric field at the growing edge of a quantum wire, and the mass distribution of solid-particle aggregates. I.

Thirty years ago, Bernard Picinbono and his colleagues carefully addressed an important problem: how an optical field is converted into a sequence of photoelectrons upon detection. Their choice of problem could not have been better, nor their timing more judicious. In a paper entitled "Photoelectron Shot Noise", published in the Journal of Mathematical Physics in 1970, when quantum optics was in its infancy, they obtained results that were to serve as an important building block in analyzing and generating many di#erent forms of light. We present some variations on the theme of cascaded stochastic processes in optics. Processus stochastiques en cascade d'importance en optique Resume--Il y a trente ans, Bernard Picinbono et ses collegues ont traite rigoureusement un probleme important : comment un champ optique est converti en une suite de photoelectrons apres detection. Leur choix de ce probleme ne pouvait pas etre meilleur et a revele un caractere pionnier. Dans un article intitule "Photoelectron Shot Noise", publie dans le Journal of Mathematical Physics en 1970, alors que l'optique quantique n'etait encore qu'a ses debuts, ils obtinrent des resultats qui constituerent un important point de depart pour analyser et generer de nombreuses et diverses formes de lumieres. Nous presentons des variations sur le theme des processus stochastiques en cascade, en optique. 1

Introduction It is usually assumed that photon events, as X-ray photons observed by a satellite, may be described by the theory of point processes (cf e. g. Matsuo, Teich and Saleh, 1983). The simplest and most common process is the homogeneous Poisson point process. Photons are usually generated in a Poisson process and in addition to that, the detection of photons is a Poisson process too. In the case of ROSAT satellite there is an additional complication. The spacecraft itself wobbles with a period of 400 seconds in order to avoid that the same parts of the sensor mosaic are constantly receiving photons from the same sources on the sky. The final result is a photon flux controlled by several Poisson processes and modulated by the spacecraft wobble. In order to study the dynamical properties of a source it is necessary to study the spectrum of variations of the Poisson parameter l (intensity of the process), at least above the wobble frequency. For frequencies from t

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