Solutions of Stochastic Differential Equations obeying the Law of the Iterated Logarithm, with applications to financial markets
John A. D. Appleby, Dublin City University, Ireland
Huizhong Wu, Dublin City University, Ireland
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.
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