Ramakrishnan, Alladi
(1950)
*Stochastic processes relating to particles distributed in a continuous infinity of states*
Mathematical Proceedings of the Cambridge Philosophical Society, 46
(4).
pp. 595-602.
ISSN 0305-0041

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Official URL: http://journals.cambridge.org/action/displayAbstra...

Related URL: http://dx.doi.org/10.1017/S0305004100026153

## Abstract

Many stochastic problems arise in physics where we have to deal with a stochastic variable representing the number of particles distributed in a continuous infinity of states characterized by a parameter E, and this distribution varies with another parameter t (which may be continuous or discrete; if t represents time or thickness it is of course continuous). This variation occurs because of transitions characteristic of the stochastic process under consideration. If the E-space were discrete and the states represented by E_{1}, E_{2}, …, then it would be possible to define a function representing the probability that there are ν_{1} particles in E_{1}, ν_{2} particles in E_{2}, …, at t. The variation of p with t is governed by the transitions defined for the process; ν_{1}, ν_{2}, … are thus stochastic variables, and it is possible to study the moments or the distribution function of the sum of such stochastic variables with the help of the p function which yields also the correlation between the stochastic variables νi.

Item Type: | Article |
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Source: | "Copyright of this article belongs to Cambridge University Press. |

ID Code: | 35427 |

Deposited On: | 04 Jul 2012 13:31 |

Last Modified: | 04 Jul 2012 13:31 |

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