Spectral analysis of a class of nonlocal elliptic operators related to Brownian motion with random jumps

Author:
Ross G. Pinsky

Journal:
Trans. Amer. Math. Soc. **361** (2009), 5041-5060

MSC (2000):
Primary 35P15, 60F10, 60J65

Published electronically:
April 16, 2009

MathSciNet review:
2506436

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a bounded domain and let denote the space of probability measures on . Consider a Brownian motion in which is killed at the boundary and which, while alive, jumps instantaneously at an exponentially distributed random time with intensity to a new point, according to a distribution . From this new point it repeats the above behavior independently of what has transpired previously. The generator of this process is an extension of the operator , defined by

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Additional Information

**Ross G. Pinsky**

Affiliation:
Department of Mathematics, Technion—Israel Institute of Technology, Haifa, 32000, Israel

Email:
pinsky@math.technion.ac.il

DOI:
http://dx.doi.org/10.1090/S0002-9947-09-04880-6

Keywords:
Principal eigenvalue,
spectral analysis,
Brownian motion,
random jumps

Received by editor(s):
June 18, 2007

Received by editor(s) in revised form:
June 3, 2008

Published electronically:
April 16, 2009

Additional Notes:
This research was supported by the M. & M. Bank Mathematics Research Fund.

Article copyright:
© Copyright 2009
American Mathematical Society

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