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In this paper, a deterministic delay differential pantograph equation (DDPE) with an unbounded memory is stochastically perturbed by an Ito-type noise. The contribution of white noise to the oscillatory behaviour of the new stochastic delay differential pantograph equation (SDDPE) is investigated. It is established that under certain conditions and with a highly positive probability, the new stochastic delay differential pantograph equation has an oscillatory solution influenced by the presence of the noise. This is not possible with the original deterministic system which has a non-oscillatory solution due to the absence of noise.

Issues in the Influence of Ito-type Noise on the Oscillation of Solutions of Delay Differential Pantograph Equations