General results on precise asymptotics for the stochastic heat equation

In this article, we investigate the precise asymptotics for complete convergence and complete moment convergence for the spatial averages of the solution to the stochastic heat equation over a Euclidean ball as the radius of the ball diverges to infinity. Some general results on precise asymptotics are obtained, which can describe the relations among the boundary function, weighted function, convergence rate, and limit value.