Identification-Inverse Problems for Partial Differential Equations: A Stochastic Formulation.
CALIFORNIA UNIV LOS ANGELES DEPT OF SYSTEM SCIENCES
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This paper presents a stochastic formulation of a class of identification problems for partial differential equations, known as inverse problems in the mathematical-physics literature. By introducing stochastic processes to model errors in observation as well as disturbance one can provide a precise formulation to interpret what appear to be ad hoc techniques, especially in the treatment of inverse problems. More importantly, one can model unknown sources as stochastic disturbances leading to more general inverse problems than considered hitherto. The report deals only with Cauchy problems for partial differential equations with continuous time observation as opposed to discrete time. Topics discussed include the following The white noise process A class of inverse problems Stochastic formulation Stochastic formulation continued source noise.
- Statistics and Probability