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2009 Solutions of Stochastic Differential Equations obeying the Law of the Iterated Logarithm, with applications to financial markets
John Appleby, Huizhong Wu
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Electron. J. Probab. 14: 912-959 (2009). DOI: 10.1214/EJP.v14-642

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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John Appleby. Huizhong Wu. "Solutions of Stochastic Differential Equations obeying the Law of the Iterated Logarithm, with applications to financial markets." Electron. J. Probab. 14 912 - 959, 2009. https://doi.org/10.1214/EJP.v14-642

Information

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

zbMATH: 1191.60069
MathSciNet: MR2497457
Digital Object Identifier: 10.1214/EJP.v14-642

Subjects:
Primary: 60H10
Secondary: 60F10, 91B28

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