期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2015
卷号：XII
期号：2
页码：551-571
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：Consider the following equation@tut(x) =12@xxut(x) + (ut(x)) _W (t; x)on an interval. Under Dirichlet boundary condition, we show that in the long run,the second moment of the solution grows exponentially fast if is large enough.But if is small, then the second moment eventually decays exponentially. If wereplace the Dirichlet boundary condition by the Neumann one, then the secondmoment grows exponentially fast no matter what is. We also provide variousextensions.
