Observability Inequality of Backward Stochastic Heat Equations for   Measurable Sets and Its Applications
  This paper aims to provide directly the observability inequality of backward stochastic heat equations for measurable sets. As an immediate application, the null controllability of the forward heat equations is obtained. Moreover, an interesting relaxed optimal actuator location problem is formulated, and the existence of its solution is proved. Finally, the solution is characterized by a Nash equilibrium of the associated game problem. 
Donghui Yang and Jie Zhong
math.OC