Understanding of relaxation process in the presence of fluctuations, with relevance to lasers and the detection of very weak signals, has been substantially improved. New insights have been obtained into stochastic resonance, with implications for ice ages, ring lasers, electron paramagnetic resonance, and the function of sensory neurons. A new theoretical approach has been developed to the problem of occasional large fluctuations, evolving time backwards from a final state and defining a prehistory probability density. Noise induced spectral narrowing and zero dispersion spectral peaks have been discovered. An improved understanding of domain growth in the presence of fluctuations has been gained. A nonequilibrium phase transition induced by coloured noise has been discovered.
It is proposed to work on the range of uncertainty inherent in the approximations required to solve certain kinds of stochastic differential equations, used to describe extremely complicated non deterministic phenomena. Comparing theoretical work with complementary analogue experiments and digital simulations it is proposed to study i) the relaxation of fluctuations in the steady state ii) the relaxation of unstable states iii) the relaxation of states that are marginally stable iv) the relaxation of metastable states of various kinds and v) the time evolution of probabilities, moments,
correlations and stochastic trajectories. In each of theses cases it is intended to establish, both experimentally and theoretically i) the relative roles of internal and external stochastic
fluctuations which are believed to be distinctively different and ii) the role of real external fluctuations for exponentially correlated Gaussian noise.