Density  of Stochastic Heat Equation and Its Approximation

The stochastic heat equation models a variety of random phenomena, such as heat conduction in various media, turbulent flow in fluid dynamics, molecular collisions in gases and liquids, and electric fluctuations in resistors. This chapter presents the density approximation for the stochastic heat equation with Lipschitz nonlinearity driven by additive noise, utilizing the accelerated exponential Euler method. A uniform weak convergence analysis, independent of test functions, is developed to investigate the convergence order of the density approximation.