# Accession Number:

## AD0606268

# Title:

## THE RANDOM FUNCTIONS OF COSMIC-RAY CASCADES,

# Descriptive Note:

# Corporate Author:

## RAND CORP SANTA MONICA CALIF

# Personal Author(s):

# Report Date:

## 1957-02-07

# Pagination or Media Count:

## 11.0

# Abstract:

The usual model for the soft component of cosmic radiation, appropriate to the assumption of complete screening, is studied. First treating the case where collision loss is neglected, the expected values for the number of electrons and photons are related to the probability distribution of a certain nonmultiplicative Markov process, limit-theorems for thiss process having an interpretation in terms of the original multiplicative process. The total energy in all electrons is shown to converge in probability to a positive constant. If collision loss is included, certain peculiarities are pointed out in the fluctuations of the number of electrons. Author