IJPAM: Volume 42, No. 2 (2008)

SYMMETRIC $\alpha$-STABLE SUBORDINATORS
AND CAUCHY PROBLEMS

Erkan Nane
Department Statistics and Probability
Michigan State University
A413 Wells Hall, East Lansing, MI 48824, USA
e-mail: nane@stt.msu.edu
url: https://www.stt.msu.edu/$\sim$nane


Abstract.We survey the results in Nane [#!nane!#] and Baeumer, Meerschaert, and Nane [#!nane-m-b!#] which deal with PDE connection of some iterated processes, and obtain a new probabilistic proof of the equivalence of the Higher order PDE's and fractional in time PDE's.

Received: August 17, 2007

AMS Subject Classification: 60J65, 60K99

Key Words and Phrases: iterated Brownian motion, PDE connection, $\alpha-$ stable process, $\alpha$-time process, fractional diffusion, Lévy process, Cauchy problem, Brownian subordinator, Caputo derivative, fractional derivative in time

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 42
Issue: 2