On oscillations of the geometric Brownian motion with time delayed drift

Uwe Küchler and Alexander Gushchin

No 2003,8, SFB 373 Discussion Papers from Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes

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 nonnegative initial process then the process generated in this way, may hit zero and may oscillate around zero infinitely often depending on properties of both drift terms and the diffusion constant.

Keywords: geometric Brownian motion; stochastic delay; differential equations; oscillations (search for similar items in EconPapers)
Date: 2003
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Journal Article: On oscillations of the geometric Brownian motion with time-delayed drift (2004)
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