Learning and estimation of Markov processes with jumps using a neural network

A nonlinear estimation problem of Markov processes with jumps from a noisy observation is discussed. A new approach to solving the estimation problem is presented using a neural network model. The neural network is designed to minimize an energy function, which consists of two terms: one is the mean square of the difference between observation data and estimates, and the other is the number of jumps contained in the estimate. The performance of the estimates obtained by the neural network depends on the ratio between the two terms. It is shown that nearly optimal state estimates are obtained by choosing a suitable value of the ratio. It is also shown that the suitable value of the ratio is learnable from samples of true processes and observation data