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Noise Induced Oscillation in Solutions of Stochastic Delay Differential Equations

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  • Appleby, John A. D.
  • Buckwar, Evelyn

Abstract

This paper studies the oscillatory properties of solutions of linear scalar stochastic delay differential equations with multiplicative noise. It is shown that such noise will induce an oscillation in the solution whenever there is negative feedback from the delay term. The zeros of the process are a countable set; the solution is differentiable at each zero, and the zeros are simple. The addition of such noise does not alter the positivity of solutions when there is positive feedback.

Suggested Citation

  • Appleby, John A. D. & Buckwar, Evelyn, 2003. "Noise Induced Oscillation in Solutions of Stochastic Delay Differential Equations," SFB 373 Discussion Papers 2003,9, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:20039
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    File URL: https://www.econstor.eu/bitstream/10419/22224/1/dpsfb20039.pdf
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    Cited by:

    1. Gushchin, Alexander A. & Küchler, Uwe, 2004. "On oscillations of the geometric Brownian motion with time-delayed drift," Statistics & Probability Letters, Elsevier, vol. 70(1), pages 19-24, October.

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