Oscillatory behaviour of solutions of linear neutral differential equations with several time lags driven by space-time noise

Abstract

The paper considers the contribution of space-time noise to the oscillatory behaviour of solutions of a linear neutral stochastic delay differential equation. It was established that under certain conditions on the time lags and their speed of adjustments, the presence of noise generates oscillation in the solution of the equation irrespective of the magnitude of the time lags. This is contrary to the comparable classical neutral differential equation which can permit a non-oscillatory solution.

Journal of the Nigerian Association of Mathematical Physics, Volume 15 (November, 2009), pp 391 - 398