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

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.

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Year of publication:	2004
Authors:	Gushchin, Alexander A. ; Küchler, Uwe
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 70.2004, 1, p. 19-24
Publisher:	Elsevier
Keywords:	Geometric Brownian motion Stochastic delay differential equations Oscillations

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005137984