Accession Number:

AD0736419

Title:

Stochastic Motion in Hilbert Space Related to a Renewal Process.

Descriptive Note:

Final rept. Jun 70-Sep 71,

Corporate Author:

HEIDELBERG UNIV (WEST GERMANY) INSTITUT FUER ANGEWANDTE MATHEMATIK

Personal Author(s):

Report Date:

1971-09-01

Pagination or Media Count:

47.0

Abstract:

The theoretical study of pressure broadening of spectral lines improves on previous work by introducing the notion of a two-sided steady state renewal process to facilitate description of a random sequence. Some properties of these processes are given and a method is described for obtaining the type process from a given situation. Working in a finite complex Hilbert space the stochastic motion of a renewal process sequence is defined and treated for the special case in which the interactions of the different groups of encounters do not overlay. The main theorem for the spectral line profile developed by this work is proven and an explicit formula for its Fourier transform is given if the frequency of encounters with the group of perturbators is not too high. Finally, the introduction of indeterminate symbology simplifies previous algebraic treatments. Author

Subject Categories:

  • Statistics and Probability
  • Atomic and Molecular Physics and Spectroscopy

Distribution Statement:

APPROVED FOR PUBLIC RELEASE