Stochastic processes in particle-number fluctuations in an electron-photon shower |
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| Authors: | S. W. Hinkley Chris P. Tsokos |
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| Affiliation: | 1. Data Systems Division, Drug Enforcement Administration, Washington, D.C.
2. Department of Mathematics, University of South Florida, 33620, Tampa, Florida
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| Abstract: | The paper is concerned with the existence and asymptotic character of the nonlinear boundary value problemdG/dt=F(t,G,F, ¦α?β¦) (1) ¦α?β¦dF/dt=g(t,G,F, ¦α?β¦)G(o,¦α?β¦)=k 1,G(∞,¦α?β¦)=k 2 (2) as ¦α?β¦→ o+ The discussion is related to the problem of particle-number fluctuations in the theory of cosmic radiation andG andF denote respectively the probability generating functions for the electron distribution in an electron-initiated and a photon-initiated shower. A solution of the system (1) satisfying the boundary conditions (2) is constructed so that specified limiting conditions are fulfilled. |
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