Stochastic Motion in Hilbert Space Related to a Renewal Process.

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)

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1971
Accession Number
AD0736419

Entities

People

  • Wilhelm Von Waldenfels

Organizations

  • Heidelberg University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Frequency
  • Hilbert Space
  • Mathematics
  • Sequences
  • Spectral Lines
  • Steady State

Fields of Study

  • Mathematics

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Statistical inference.
  • Systems Analysis and Design

Technology Areas

  • Space