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Solutions of Stochastic Differential Equations obeying the Law of the Iterated Logarithm, with applications to financial markets


 
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1. Title Title of document Solutions of Stochastic Differential Equations obeying the Law of the Iterated Logarithm, with applications to financial markets
 
2. Creator Author's name, affiliation, country John A. D. Appleby; Dublin City University, Ireland
 
2. Creator Author's name, affiliation, country Huizhong Wu; Dublin City University, Ireland
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) stochastic differential equations; Brownian motion; Law of the Iterated Logarithm; Motoo's theorem; stochastic comparison principle; stationary processes; inefficient market
 
3. Subject Subject classification 60H10; 60F10; 91B28
 
4. Description Abstract By using a change of scale and space, we study a class of stochastic differential equations (SDEs) whose solutions are drift--perturbed and exhibit asymptotic behaviour similar to standard Brownian motion. In particular sufficient conditions ensuring that these processes obey the Law of the Iterated Logarithm (LIL) are given. Ergodic--type theorems on the average growth of these non-stationary processes, which also depend on the asymptotic behaviour of the drift coefficient, are investigated. We apply these results to inefficient financial market models. The techniques extend to certain classes of finite--dimensional equation.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) We gratefully acknowledge the support of this work by Science Foundation Ireland under the Research Frontiers Programme grant RFP/MAT/0018 ``Stochastic Functional Differential Equations with Long Memory'' and under the Mathematics Initiative 2007 grant 07
 
7. Date (YYYY-MM-DD) 2009-04-27
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/642
 
10. Identifier Digital Object Identifier 10.1214/EJP.v14-642
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 14
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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