Abstract
The purpose of this paper is to study the state and free boundary estimates for distributed parameter systems with stochastic free boundary.
First, the mathematical model of the distributed parameter system with the stochastic free boundary is transformed to the stochastic distributed parameter system with the fixed domain by the change of variable and furthermore its existence theorem and regularity of the solution are established. Secondly, both the state and free boundary estimator equations are derived by using the martingale and innovation approaches.
