NONLINEAR NOISE EXCITATION OF INTERMITTENT STOCHASTIC PDES AND THE TOPOLOGY OF LCA GROUPS
成果类型：
Article
署名作者：
Khoshnevisan, Davar; Kim, Kunwoo
署名单位：
Utah System of Higher Education; University of Utah
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/14-AOP925
发表日期：
2015
页码：
1944-1991
关键词：
摘要：
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.