Nonlinear noise excitation of intermittent stochastic PDEs and the topology of LCA groups
SCIE
SCOPUS
- Title
- Nonlinear noise excitation of intermittent stochastic PDEs and the topology of LCA groups
- Authors
- Khoshnevisan, D; Kim, K
- Date Issued
- 2015-07
- Publisher
- The Institute of Mathematical Statistics
- Abstract
- Consider the stochastic heat equation partial derivative(t)u = Lu + lambda sigma (u)xi, where L denotes the generator of a Levy process on a locally compact Hausdorff Abelian group G, sigma : R -> R is Lipschitz continuous, lambda >> 1 is a large parameter, and xi denotes space time white noise on R+ x G.
The main result of this paper contains a near-dichotomy for the (expected squared) energy E(parallel to u(t)parallel to(2)(L2(G))) of the solution. Roughly speaking, that dichotomy says that, in all known cases where u is intermittent, the energy of the solution behaves generically as exp{const.lambda(2)} when G is discrete and > exp(const.lambda(4)) when G is connected.
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/36756
- DOI
- 10.1214/14-AOP925
- ISSN
- 0091-1798
- Article Type
- Article
- Citation
- ANNALS OF PROBABILITY, vol. 43, no. 4, page. 1944 - 1991, 2015-07
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