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Reconstruction of stochastic nonlinear models from trajectory measurements

Research output: Contribution to journalJournal article

Published

<mark>Journal publication date</mark>2005
<mark>Journal</mark>Proceedings of SPIE
Volume5845
Number of pages9
Pages173-181
<mark>Original language</mark>English

Abstract

We consider the following general problem of applied stochastic nonlinear dynamics. We observe a time series of signals y(t) = y(t0+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.

Bibliographic note

Copyright 2005 Society of Photo-Optical Instrumentation Engineers. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited. http://dx.doi.org/10.1117/12.610457