Higher order PDE's and iterated processes

Author:
Erkan Nane

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

Published electronically:
December 20, 2007

MathSciNet review:
2373329

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Abstract | References | Similar Articles | Additional Information

Abstract: We introduce a class of stochastic processes based on symmetric -stable processes, for . These are obtained by taking Markov processes and replacing the time parameter with the modulus of a symmetric -stable process. We call them -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 -time processes to some higher order PDE's for rational. We also obtain the PDE connection of subordinate killed Brownian motion in bounded domains of regular boundary.

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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

Email:
enane@math.purdue.edu

DOI:
https://doi.org/10.1090/S0002-9947-07-04437-6

Keywords:
Iterated Brownian motion,
exit time,
PDE connection,
$\alpha$-stable process,
$\alpha$-time process,
subordinate killed Brownian motion.

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.

Article copyright:
© Copyright 2007
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.