Bayesian inverse problems in measure spaces with application to Burgers and Hamilton-Jacobi equations with white noise forcing. (English) Zbl 1236.93149
Summary: This paper formulates Bayesian inverse problems for inference in a topological measure space given noisy observations. Conditions for the validity of the Bayes’ formula and the well posedness of the posterior measure are studied. The abstract theory is then applied to Burgers and Hamilton-Jacobi equations on a semi-infinite time interval with forcing functions which are white noise in time. Inference is made on the white noise forcing, assuming the Wiener measure as the prior.
MSC:
93E12 | Identification in stochastic control theory |
35Q35 | PDEs in connection with fluid mechanics |