Identification - - Inverse Problems for Partial Differential Equations : a Stochastic Formulation

This paper presents a stochastic formulation of a class of identification problems for partial differential equations, known as 'inverse' problems in the mathematicalphysics literature. By introducing stochastic processes to model errors in observation as well as 'disturbance' we can provide a precise formulation to interpret what appear to be 'ad hoc' techniques, especially in the treatment of 'inverse' problems. More importantly, we can model unknown sources as stochastic disturbances leading to more general 'inverse' problems than considered hitherto.