The representation of non-linear stochastic systems with applications to filtering
John M. Clark · Spiral (Imperial College London) · 1966
Physical processes can often be described by a system of ordinary differential equations excited by random disturbances with short correlation times.It is shown in this thesis that such processes can be approximated, in the sense that the second moment of error is small, by Markov diffusion processes of the same dimension.In the approximation the random disturbances are characterised by a matrix which is an integral of their cross-correlation function, but which is not in general the cross-spectral density.If this characteristic matrix is symmetric, the Stratonovich stochastic differential equation of the diffusion approximation is similar in form to the ordinary differential equation of the physical process.In computer simulations the ordinary differential equation of a physical process can be used as the programming model if the characteristic matrices of the disturbances and the computer noise source are both symmetric and of the same rank.With the aid of diffusion approximations, much of the theory of the filtering of diffusion processes can be applied to .problems in the filtering of physical processes. CONTENTS *In particular this satisfied if a(s) and F(s) are a.c.continuous.