Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-24T12:24:38.959Z Has data issue: false hasContentIssue false
  • English
  • Français

Stochastic processes relating to particles distributed in a continuous infinity of states

Published online by Cambridge University Press:  24 October 2008

Alladi Ramakrishnan
Alladi Ramakrishnan
Affiliation:
Department of MathematicsUniversity of Manchester
Get access Rights & Permissions [Opens in a new window]

Extract

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 E1, E2, …, then it would be possible to define a function

representing the probability that there are ν1 particles in E1, ν2 particles in E2, …, at t. The variation of π with t is governed by the transitions defined for the process; ν1, ν2, … 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 π function which yields also the correlation between the stochastic variables νi.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 46 , Issue 4 , October 1950 , pp. 595 - 602
Copyright
Copyright © Cambridge Philosophical Society 1950

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Bhabha, H. J. and Heitler, W.Proc. Roy. Soc. A, 159 (1937), 432.Google Scholar
(2)Carlson, J. F. and Oppenheimer, J. R.Phys. Rev. 51 (1937), 220.CrossRefGoogle Scholar
(3)Landau, L. and Rumer, G.Proc. Roy. Soc. A, 166 (1938), 213.Google Scholar
(4)Bhabha, H. J. and Chakrabarthi, S. K.Proc. Roy. Soc. A, 181 (1943), 267.Google Scholar
(5)Scott, W. T. and Uhlenbeck, C. E.Phys. Rev. 62 (1942), 497.CrossRefGoogle Scholar
(6)Heitler, W.Quantum theory of radiation, 2nd ed. (Oxford, 1944).Google Scholar
(7)Arley, N.On the theory of stochastic processes and their application to the theory of coamic radiation (Copenhagen, 1943), p. 149.Google Scholar
(8)Stevens, W. L.Ann. Eugen., London, 8 (1937–1939), 57.CrossRefGoogle Scholar
(9)Kendall, D. G.J. R. Statist. Soc. (B), 11 (1949), 230.Google Scholar
(10)Kendall, D. G.J. R. Statist. Soc. (B), 12 (1950) (in the Press).Google Scholar
(11)Bartlett, M. S. and Kendall, D. G.Proc. Cambridge Phil. Soc. (in the Press).Google Scholar