Direct and Inverse Problems for PDEs with Random Coefficients - Abstract
A recent framework for the optimal control of stochastic processes based on the Fokker-Planck-Kolmogorov (FPK) equation is introduced. This technique allows to control the shape of the probability density function of the stochastic process. By using this ability, the problem of the calibration of a Lévy process is handled. The calibration is formulated as a minimization problem of a distance functional with constraint given by the FPK equation. The numerical method for the solution of the optimization problem is discussed. Finally, some applications to test problem and real stochastic data show the ability of the proposed technique to calculate the calibration values of the model.