Abstract
We study the identification problem of a spatially varying discontinuous parameter in stochastic hyperbolic systems under noisy partial observations. The consistency property of the maximum likelihood estimate(M.L.E.) for a discontinuous coefficient is proved by using the method of sieves. A typical hyperbolic equation does not have a suitable regularity property of the solution with respect to a parameter to support the consistency property of M.L.E. Introducing the parabolic regu-larization technique, we show that the derived finite-dimensional M.L.E. converges to the infinite-dimensional M.L.E. under some conditions. Numerical examples are demonstrated to check the theoretical results.
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