Abstract
Intermittency arises typically in random fields of multiplicative type like the solution of stochastic heat equation. This paper investigates whether the stochastic heat equation with multiplicative noise under a discretization could inherit the dynamical behavior in particular the weak intermittency of the original equation. The exact solution of the stochastic heat equation with multiplicative noise is proved to admit weak intermittency with a specific index of Lyapunov exponents. We prove the existence of the weak intermittency for stochastic heat equation under a class of discretizations, and further the preservation of the index of Lyapunov exponents of the exact solution by a renewal approach, provided in addition that the initial datum is a positive constant and the spatial partition number is large.
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