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An ergodic theorem of a parabolic Anderson model driven by Lévy noise
Frontiers of Mathematics in China, Volume: 6, Issue: 6, Pages: 1147 - 1183
Swansea University Author: Jiang-lun Wu
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DOI (Published version): 10.1007/s11464-011-0124-y
Abstract
In this paper, we study an ergodic theorem of a parabolic Andersen model driven by Lévy noise. Under the assumption that A = (a(i, j))i,j∈S is symmetric with respect to a σ-finite measure gp, we obtain the long-time convergence to an invariant probability measure νh starting from a bounded nonnegati...
| Published in: | Frontiers of Mathematics in China |
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| ISSN: | 1673-3452 1673-3576 |
| Published: |
Berlin, Heidelberg
Higher Education Press and Springer-Verlag
2011
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| Online Access: |
Check full text
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa8021 |
| Abstract: |
In this paper, we study an ergodic theorem of a parabolic Andersen model driven by Lévy noise. Under the assumption that A = (a(i, j))i,j∈S is symmetric with respect to a σ-finite measure gp, we obtain the long-time convergence to an invariant probability measure νh starting from a bounded nonnegative A-harmonic function h based on self-duality property. Furthermore, under some mild conditions, we obtain the one to one correspondence between the bounded nonnegative A-harmonic functions and the extremal invariant probability measures with finite second moment of the nonnegative solution of the parabolic Anderson model driven by Lévy noise, which is an extension of the result of Y. Liu and F. X. Yang. |
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| Keywords: |
Parabolic Anderson model, ergodic theorem, invariant measure, Lévy noise, self-duality. |
| College: |
Faculty of Science and Engineering |
| Issue: |
6 |
| Start Page: |
1147 |
| End Page: |
1183 |