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Modeling Continuous Time Series Driven by Fractional Gaussian Noise

  • Winston C. Chow
  • Edward J. Wegman
Conference paper
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 139)

Abstract

We consider the stochastic differential equations, dX(t) = θX(t)dt + dB H (t); t > 0, and dX(t) = θ(t)X(t)dt + dB H (t); t > 0 where B H (t) is fractional Brownian motion. We find solutions for these differential equations and show the existence of the integrals related to these solutions. We then show that B H (t) is not a martingale. This implies that several conventional methods for defining integrals on fractional Brownian motion are inadequate. We demonstrate the existence of an estimator for θ which depends on the existence of integrals of certain integrals with respect to fractional Brownian motion. We conclude by showing the existence and Riemann sum approximations for these integrals.

Keywords

Brownian Motion Stochastic Differential Equation Cauchy Sequence Synthetic Aperture Radar Fractional Brownian Motion 
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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Copyright information

© Springer-Verlag New York, LLC 2004

Authors and Affiliations

  • Winston C. Chow
  • Edward J. Wegman

There are no affiliations available

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