An observability inequality for a stochastic heat cascade equations and application

In this paper, by means of Carleman estimates and the usual energy estimate, we obtain an observability inequality for a cascade stochastic heat equations. Furthermore, the constant in the observability inequality is estimated by an explicit function of the norm of the involved coefficients in the equations. Also, we apply our observability estimate to obtain the existence of insensitizing controls for a forward stochastic heat equations.