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 Electronic Communications in Probability > Vol. 9 (2004) > Paper 12 open journal systems 


Oscillation and Non-oscillation in Solutions of Nonlinear Stochastic Delay Differential Equations

John A. D. Appleby, Dublin City University
Conall Kelly, Dublin City University, Dublin, Ireland


Abstract
This paper studies the oscillation and nonoscillation of solutions of a nonlinear stochastic delay differential equation, where the noise perturbation depends on the current state, and the drift depends on a delayed argument. When the restoring force towards equilibrium is relatively strong, all solutions oscillate, almost surely. However, if the restoring force is superlinear, positive solutions exist with positive probability, and for suitably chosen initial conditions, the probability of positive solutions can be made arbitrarily close to unity.


Full text: PDF

Pages: 106-118

Published on: October 6, 2004


Bibliography
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Electronic Communications in Probability. ISSN: 1083-589X