Publication Cover
Stochastics
An International Journal of Probability and Stochastic Processes
Volume 85, 2013 - Issue 2
127
Views
6
CrossRef citations to date
0
Altmetric
Original Articles

Spectral representation of transition density of Fisher–Snedecor diffusion

, &
Pages 346-369 | Received 03 Feb 2011, Accepted 07 Feb 2013, Published online: 11 Mar 2013
 

Abstract

We analyse spectral properties of an ergodic heavy-tailed diffusion with the Fisher–Snedecor invariant distribution and compute spectral representation of its transition density. The spectral representation is given in terms of a sum involving finitely many eigenvalues and eigenfunctions (Fisher–Snedecor orthogonal polynomials) and an integral over the absolutely continuous spectrum of the corresponding Sturm–Liouville operator. This result enables the computation of the two-dimensional density of the Fisher–Snedecor diffusion as well as calculation of moments of the form , where m and n are at most equal to the number of Fisher–Snedecor polynomials. This result is particularly important for explicit calculations associated with this process.

Acknowledgements

The research was partly supported by the EPSRC grant EP/D057361 and Marie Curie grant of European Communities PIRSES-GA-2008-230804.

Log in via your institution

Log in to Taylor & Francis Online

PDF download + Online access

  • 48 hours access to article PDF & online version
  • Article PDF can be downloaded
  • Article PDF can be printed
USD 61.00 Add to cart

Issue Purchase

  • 30 days online access to complete issue
  • Article PDFs can be downloaded
  • Article PDFs can be printed
USD 1,425.00 Add to cart

* Local tax will be added as applicable

Related Research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.