Stochastic Motion in Hilbert Space Related to a Renewal Process.
Final rept. Jun 70-Sep 71,
HEIDELBERG UNIV (WEST GERMANY) INSTITUT FUER ANGEWANDTE MATHEMATIK
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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
- Statistics and Probability
- Atomic and Molecular Physics and Spectroscopy