Stochastic Parabolic Partial Differential Equations: Convergence And Stability

Abstract

In this work, the convergence and stability analysis are investigated for stochastic parabolic partial differential equations of Ito-type. A very general comparison theorem is obtained in the context of vector Lyapunov-like functions and differential inequalities. Furthermore, this comparison theorem has been applied to derive sufficient conditions for various concepts of stability and convergence of the equilibrium state of the system. In addition, an example is given to illustrate the significance of the presented results.