Maccone first KLT theorem: KLT of all timerescaled Brownian motions

Chapter
Part of the Springer Praxis Books book series (PRAXIS)

Abstract

In Section 21.4 the problem of finding the KL expansion of standard Brownian motion was solved completely. That was possible because the differential equation for the eigenfunctions was just a simple harmonic oscillator equation, whose solution is trivial.

Keywords

Integral Equation Brownian Motion Bessel Function Gaussian Process Stability Criterion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    C. Maccone, “Eigenfunctions and Energy for Time-Rescaled Gaussian Processes,” Bollettino dell’Unione Matematica Italiana, Series 6, 3-A (1984), 212–219.Google Scholar
  2. 2.
    A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher Transcendental Functions, Vol. 2, McGraw-Hill, New York, 1952.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.International Academy of Astronautics and Istituto Nazionale di AstrofisicaTorino (Turin)Italy

Personalised recommendations