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      Distance between the fractional Brownian motion and the space of adapted Gaussian martingales

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      Nonlinear Analysis: Modelling and Control
      Vilnius University Press

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          Abstract

          We consider the distance between the fractional Brownian motion defined on the interval [0,1] and the space of Gaussian martingales adapted to the same filtration. As the distance between stochastic processes, we take the maximum over [0,1] of mean-square deviances between the values of the processes. The aim is to calculate the function a in the Gaussian martingale representation ∫0ta(s)dWs that minimizes this distance. So, we have the minimax problem that is solved by the methods of convex analysis. Since the minimizing function a can not be either presented analytically or calculated explicitly, we perform discretization of the problem and evaluate the discretized version of the function a numerically.

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          Author and article information

          Journal
          Nonlinear Analysis: Modelling and Control
          NAMC
          Vilnius University Press
          2335-8963
          1392-5113
          June 27 2019
          June 27 2019
          : 24
          : 4
          Article
          10.15388/NA.2019.4.9
          b109db50-8d07-4b00-9e82-52283acd7c9f
          © 2019

          All content is freely available without charge to users or their institutions. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles in this journal without asking prior permission of the publisher or the author. Articles published in the journal are distributed under a http://creativecommons.org/licenses/by/4.0/.


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