Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Higher order PDE’s and iterated processes
HTML articles powered by AMS MathViewer

by Erkan Nane PDF
Trans. Amer. Math. Soc. 360 (2008), 2681-2692 Request permission

Abstract:

We introduce a class of stochastic processes based on symmetric $\alpha$-stable processes, for $\alpha \in (0,2]$. These are obtained by taking Markov processes and replacing the time parameter with the modulus of a symmetric $\alpha$-stable process. We call them $\alpha$-time processes. They generalize Brownian time processes studied in Allouba and Zheng (2001), Allouba (2002), (2003), and they introduce new interesting examples. We establish the connection of $\alpha$-time processes to some higher order PDE’s for $\alpha$ rational. We also obtain the PDE connection of subordinate killed Brownian motion in bounded domains of regular boundary.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 60J65, 60K99
  • Retrieve articles in all journals with MSC (2000): 60J65, 60K99
Additional Information
  • Erkan Nane
  • Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47906
  • Address at time of publication: Department of Statistics and Probability, A 413 Wells Hall, Michigan State University, East Lansing, Michigan 48824
  • MR Author ID: 782700
  • Email: enane@math.purdue.edu
  • Received by editor(s): May 8, 2006
  • Published electronically: December 20, 2007
  • Additional Notes: This work was supported in part by NSF Grant # 9700585-DMS.
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 360 (2008), 2681-2692
  • MSC (2000): Primary 60J65, 60K99
  • DOI: https://doi.org/10.1090/S0002-9947-07-04437-6
  • MathSciNet review: 2373329