Electronic Journal of Probability
- Electron. J. Probab.
- Volume 14 (2009), paper no. 33, 912-959.
Solutions of Stochastic Differential Equations obeying the Law of the Iterated Logarithm, with applications to financial markets
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.
Electron. J. Probab., Volume 14 (2009), paper no. 33, 912-959.
Accepted: 27 April 2009
First available in Project Euclid: 1 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]
Secondary: 60F10: Large deviations 91B28
This work is licensed under aCreative Commons Attribution 3.0 License.
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