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Maximum Likelihood Estimation in Fractional Diffusions

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1923)

In view of recent empirical findings of long memory in finance, it becomes necessary to extend the diffusion models to processes having long-range dependence. One way is to use stochastic differential equations with fractional Brownian motion (fBm) driving term, with Hurst index greater than 1/2, the solution of which is called fractional diffusion. The fBm being not a Markov process and not a semimartingale (except for the case where Hurst index is 1/2), the classical Itô calculus is not applicable to develop its theory.

Keywords

  • Brownian Motion
  • Maximum Likelihood Estimation
  • Maximum Likelihood Estimator
  • Fractional Brownian Motion
  • Iterate Logarithm

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 2008 Springer-Verlag Berlin Heidelberg

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(2008). Maximum Likelihood Estimation in Fractional Diffusions. In: Parameter Estimation in Stochastic Differential Equations. Lecture Notes in Mathematics, vol 1923. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74448-1_6

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