On oscillations of the geometric Brownian motion with time-delayed drift

Alexander Gushchin and Uwe Küchler

Statistics & Probability Letters, 2004, vol. 70, issue 1, 19-24

Abstract: The geometric Brownian motion is the solution of a linear stochastic differential equation in the Itô sense. If one adds to the drift term a possible nonlinear time-delayed term and starts with a non-negative initial process then the process generated in this way, may hit zero and may oscillate around zero infinitely many times depending on properties of both the drift terms and the diffusion constant.

Keywords: Geometric; Brownian; motion; Stochastic; delay; differential; equations; Oscillations (search for similar items in EconPapers)
Date: 2004
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