Thesis-1981-Schagen.pdf (3.88 MB)

Download file# Theory and applications of multi-dimensional stationary stochastic processes

thesis

posted on 30.05.2014, 14:03 authored by Ian P. SchagenThe theory of stationary stochastic processes in several dimensions
has been investigated to provide a general model which may be applied to
various problems which involve unknown functions of several variables.
In particular, when values of the function are known only at a finite set
of points, treating the unknown function as a realisation of a stationary
stochastic process leads to an interpolating function which reproduces the
values exactly at the given points. With suitable choice of auto-correlation
for the model, the interpolating function may also he shown to be continuous
in all its derivatives everywhere. A few parameters only need to be found
for the interpolator, and these may be estimated from the given data.
One problem tackled using such an interpolator is that of automatic
contouring of functions of two variables from arbitrarily scattered data
points. A "two-stage" model was developed, which incorporates a long-range "trend" component as well as a shorter-range "residual" term. This leads
to a contouring algorithm which gives good results with difficult data.
The second area of application is that of optimisation, particularly of
objective functions which are expensive to compute. Since the interpolator
gives an estimate of the derivatives with little work, it is simple to
optimise it using conventional techniques, and to re-evaluate the true
function at the apparent optimum point. An iterative algorithm along these
lines gives good results with test functions, especially with fuactions of
more than two variables. A program has been developed whicj incorporates
both the optimisation and contouring applications into a single peckage.
Finally, the theory of excursions of a stationary process above a
fixed level has been applied to the problem of modelling the occurrence
of oilfields, with special reference to their spatial distribution and
tendency to cluster. An intuitively reasonable model with few parameters
has been developed and applied to North Sea data, with interesting results.

## History

## School

- Science

## Department

- Computer Science