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 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.

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Year of publication:	2003
Authors:	Küchler, Uwe ; Gushchin, Alexander A.
Publisher:	Berlin : Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes
Subject:	Stochastischer Prozess \| Analysis \| Theorie \| stochastic delay differential equation \| geometric Brownian motion \| stochastic delay \| differential equations \| oscillations

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Series:	SFB 373 Discussion Paper ; 2003,8
Type of publication:	Book / Working Paper
Type of publication (narrower categories):	Working Paper
Language:	English
Other identifiers:	379243954 [GVK] hdl:10419/22223 [Handle] RePEc:zbw:sfb373:20038 [RePEc]
Source:	EconStor

Persistent link: https://www.econbiz.de/10010296444