Noise Induced Oscillation in Solutions of Stochastic Delay Differential Equations
AbstractThis 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. --
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Bibliographic InfoPaper provided by Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes in its series SFB 373 Discussion Papers with number 2003,9.
Date of creation: 2003
Date of revision:
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- Küchler, Uwe & Gushchin, Alexander A., 2003.
"On oscillations of the geometric Brownian motion with time delayed drift,"
SFB 373 Discussion Papers
2003,8, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- 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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