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• W2310814749 abstract "continuous stochastic processes. The homogeneous Poisson point process (HPP) is characterized by a single quantity, its rate, which is constant. One of its distinguishing features is that it evolves in time without aftereffects. This means that the occurrence times and number of events before an arbitrary time have no bearing on the subsequent occurrence times and number of events. It is said to have zero memory. Because of its simple properties, the HPP turns out to be a suitable building block for more complex point processes that appear to resemble the Poisson process little, if at all. We all recall, no doubt, a very important property of this process: pass an HPP through a lined filter and out comes shot noise. This result is probably just a shade younger than electrical engineering itself. There are many generalizations of the H€T. One case that has been studied extensively is the doubly stochastic Poisson point process (DSPP), which diffels from the HPP in that the rate is no longer constant. Rather, it takes on a stochastic nature of its own. This process was fit examined by Cox (and by Bartlett in the discussion to Cox’s paper) [41. Cox provided an example of its use in textile technology. The designation DSPP wa~ introduced to emphasize that two kinds of randomness occur: randomness associated with the Poisson point process itself and an independent randomness associated with its rate. The earliest connection of the DSPP with electrical engineering appears to be in the work of Darling and Siegert [SI and Siegert [61. The DSPP subsequently became the basis for understanding the photodetection of light, and many of the early papers in this area [7] -[ 151 drew heavily on results derived in connection with classical radio receiver communications and noise [ 161 -[ 181. At the same time, the DSPP arose in the context of the detection of acoustic noise in the auditory system [ 19 I . , A number of excellent secondary sources, detailing the history and properties of the DSPP, are available [3], [201-[271. In certain areas of study, multiplication effects in point processes play an important role; in most such cases, a given (primary) point process is multiplied in some fashion to give rise to a second (subsidiary) point process. Cathodoluminescence 128 I , [ 29 I , which is responsible for the television, oscilloscope, and radar images, provides a simple but impopt" @default.
• W2310814749 created "2016-06-24" @default.
• W2310814749 creator A5071873130 @default.
• W2310814749 date "1982-01-01" @default.
• W2310814749 modified "2023-09-27" @default.
• W2310814749 title "Multiplied-Poisson Noise in Pulse, Particle, and" @default.
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