Electronic Journal of Probability

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

John Appleby and Huizhong Wu

Full-text: Open access

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.

Article information

Source
Electron. J. Probab., Volume 14 (2009), paper no. 33, 912-959.

Dates
Accepted: 27 April 2009
First available in Project Euclid: 1 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464819494

Digital Object Identifier
doi:10.1214/EJP.v14-642

Mathematical Reviews number (MathSciNet)
MR2497457

Zentralblatt MATH identifier
1191.60069

Subjects
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]
Secondary: 60F10: Large deviations 91B28

Keywords
stochastic differential equations Brownian motion Law of the Iterated Logarithm Motoo's theorem stochastic comparison principle stationary processes inefficient market

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Appleby, John; Wu, Huizhong. Solutions of Stochastic Differential Equations obeying the Law of the Iterated Logarithm, with applications to financial markets. Electron. J. Probab. 14 (2009), paper no. 33, 912--959. doi:10.1214/EJP.v14-642. https://projecteuclid.org/euclid.ejp/1464819494


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