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

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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

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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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