# On secondary processes generated by a Poisson process and their applications in physics

On secondary processes generated by a Poisson process and their applications in physics ON SECONDARY PROCESSES GENERATED BY A POISSON PROCESS AND THEIR APPLICATIONS IN PHYSICS By LAJOS TAKA.CS (Budapest) (Presented by A. R~NYI) w 1. Formulation of the problem Let us consider a stochastic process of the Poisson type. Let the den- sity of the occurrence of the events be a non-negative, continuous and bounded function /,(u) of the time parameter u. The average number of the events occurring in the time interval (0, t) is, as well known, (1) 3(0 = du and the probability of exactly k events occurring in the time interval (0, t)is (2) P(t, k) e .,e~ [3 (t)] ': (k = 0, 1, 2, .). k! "" The present work is devoted to investigating the following problem. Suppose that every event in the Poisson process is the starting point of a signal (random pulse). Let the progress in time of the amplitude of a signal be f(u,z) where u is the time counted from the beginning of the signal and the parameter Z is a random variable. We suppose that the para- meters belonging to different events are mutually independent rarldom vari- ables with the common distribution function P(Z ~ x)=H(x). We suppose, finally, that http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematica Academiae Scientiarum Hungarica Springer Journals

# On secondary processes generated by a Poisson process and their applications in physics

, Volume 5 (4) – Jul 16, 2005
34 pages      /lp/springer-journals/on-secondary-processes-generated-by-a-poisson-process-and-their-R4Pwy14mzb
Publisher
Springer Journals
Subject
Mathematics; Mathematics, general
ISSN
0001-5954
eISSN
1588-2632
DOI
10.1007/BF02020410
Publisher site
See Article on Publisher Site

### Abstract

ON SECONDARY PROCESSES GENERATED BY A POISSON PROCESS AND THEIR APPLICATIONS IN PHYSICS By LAJOS TAKA.CS (Budapest) (Presented by A. R~NYI) w 1. Formulation of the problem Let us consider a stochastic process of the Poisson type. Let the den- sity of the occurrence of the events be a non-negative, continuous and bounded function /,(u) of the time parameter u. The average number of the events occurring in the time interval (0, t) is, as well known, (1) 3(0 = du and the probability of exactly k events occurring in the time interval (0, t)is (2) P(t, k) e .,e~ [3 (t)] ': (k = 0, 1, 2, .). k! "" The present work is devoted to investigating the following problem. Suppose that every event in the Poisson process is the starting point of a signal (random pulse). Let the progress in time of the amplitude of a signal be f(u,z) where u is the time counted from the beginning of the signal and the parameter Z is a random variable. We suppose that the para- meters belonging to different events are mutually independent rarldom vari- ables with the common distribution function P(Z ~ x)=H(x). We suppose, finally, that

### Journal

Acta Mathematica Academiae Scientiarum HungaricaSpringer Journals

Published: Jul 16, 2005

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