EconPapers    
Economics at your fingertips  
 

Exponential stability in p-th mean of solutions, and of convergent Euler-type solutions, of stochastic delay differential equations

Christopher T. H. Baker and Evelyn Buckwar

No 2001,94, SFB 373 Discussion Papers from Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes

Abstract: Results are presented on the stability of solutions of stochastic delay differential equations with multiplicative noise and of convergent numerical solutions obtained by a a method of Euler-Maruyama type. An attempt is made to provide a fairly self-contained presentation. A basic concept of the stability of a solution of an evolutionary stochastic delay differential equation is concerned with the sensitivity of the solution to perturbations in the initial function. We recall the stability definitions considered herein and show that an inequality of Halanay type (derivable via comparison theory)j and deterministic results can be employed to derive stability conditions for solutions of suitable equations. In practice, dosed form solutions of stochastic delay differential equations are unlikely to he available. In the second part of the paper a stability theory for numerical solutions (solutions of Euler type) is considered. A convergence result is recalled for completeness and new stability results are obtained using a discrete analogue of the continuous Halanay-type inequality and results for a deterministic recurrence relation. Various results for stochastic (ordinary) differential equations with no time lag or for deterministic delay differential equations can he deduced from the results given here.

Date: 2001
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.econstor.eu/bitstream/10419/62674/1/725962259.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:zbw:sfb373:200194

Access Statistics for this paper

More papers in SFB 373 Discussion Papers from Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes Contact information at EDIRC.
Bibliographic data for series maintained by ZBW - Leibniz Information Centre for Economics ().

 
Page updated 2025-03-20
Handle: RePEc:zbw:sfb373:200194