Georgiou, N., Joseph, M., Khoshnevisan, D. et al. (1 more author) (2015) Semi-discrete semi-linear parabolic spdes. Annals of Applied Probability, 25 (5). 2959 - 3006. ISSN 1050-5164
Abstract
© Institute of Mathematical Statistics, 2015. Consider an infinite system (eqution presented) of interacting Itǒ diffusions, started at a nonnegative deterministic bounded initial profile. We study local and global features of the solution under standard regularity assumptions on the nonlinearity σ. We will show that, locally in time, the solution behaves as a collection of independent diffusions. We prove also that the kth moment Lyapunov exponent is frequently of sharp order κ<inf>2</inf>, in contrast to the continuous-space stochastic heat equation whose kth moment Lyapunov exponent can be of sharp order κ<inf>3</inf>. When the underlying walk is transient and the noise level is sufficiently low, we prove also that the solution is a.s. uniformly dissipative provided that the initial profile is in 1(Zd ).
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2015 Institute of Mathematical Statistics. Reproduced in accordance with the publisher's self-archiving policy.
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Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 08 Oct 2015 13:05 |
Last Modified: | 16 Nov 2015 11:49 |
Published Version: | http://dx.doi.org/10.1214/14-AAP1065 |
Status: | Published |
Publisher: | Institute of Mathematical Statistics |
Refereed: | Yes |
Identification Number: | 10.1214/14-AAP1065 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:90261 |