Reconstruction of stochastic nonlinear dynamical models from trajectory measurements (Invited Paper)

We consider the following general problem of applied stochastic nonlinear dynamics (see e.g.(1)). We observe a time series of signals y(t) = y(t(0) + hn) corrupted by noise. The actual state and the nonlinear vector field of the dynamical system is not known. The question is how and with what accuracy can we determine x(t) and functional form of f (x). In this talk we discuss a novel approach to the solution of this problem based on the application of the path-integral approach to the full Bayesian inference. We demonstrate a reconstruction of a dynamical state of a system from corrupted by noise measurements. Next we reconstruct the corresponding nonlinear vector field. The emphasis are on the theoretical analysis. The results are compared with the results of earlier research.