The estimation of parameters for stochastic differential equations using neural networks

Abstract

In this article artificial neural network (ANN) is used to estimate parameters of stochastic differential equations (SDEs) given the discrete output variables of the equations. Some techniques are used to improve ANN performance in data preparation and ANN training procedure. In particular, an increase in the number of Wiener processes used to create training data set raises the accuracy of estimates significantly. The analysis of the results suggests that ANN can predict parameters of SDEs accurately under certain noise level regimes using an appropriate network architecture.