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2004 Oscillation and Non-oscillation in Solutions of Nonlinear Stochastic Delay Differential Equations
John Appleby, Conall Kelly
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Electron. Commun. Probab. 9: 106-118 (2004). DOI: 10.1214/ECP.v9-1115

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.

Citation

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John Appleby. Conall Kelly. "Oscillation and Non-oscillation in Solutions of Nonlinear Stochastic Delay Differential Equations." Electron. Commun. Probab. 9 106 - 118, 2004. https://doi.org/10.1214/ECP.v9-1115

Information

Accepted: 6 October 2004; Published: 2004
First available in Project Euclid: 26 May 2016

zbMATH: 1060.60059
MathSciNet: MR2108857
Digital Object Identifier: 10.1214/ECP.v9-1115

Subjects:
Primary: 60H10
Secondary: 34K11, 34K50

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