On Simulation of a Fractional Ornstein–Uhlenbeck Process of the Second Kind by the Circulant Embedding Method

  • José Igor Morlanes
  • Andriy AndreevEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 271)


We demonstrate how to utilize the Circulant Embedding Method (CEM) for simulation of fractional Ornstein–Uhlenbeck process of the second kind (\({ fOU}_2\)). The algorithm contains two major steps. First, the relevant covariance matrix is embedded into a circulant one. Second, a sample from the \({ fOU}_2\) is obtained by means of fast Fourier transform applied on the circulant extended matrix. The main goal of this paper is to explain both steps in detail. As a result, we obtain an accurate and an efficient algorithm for generating \({ fOU}_2\) random vectors. We also indicate that the above described procedure can be extended to applications with non-Gaussian marginals.


Fractional Brownian motion Fractional Ornstein–Uhlenbeck process Circulant embedding method Simulation 



We thank Michael Carlson for assistance with final English check.


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of StatisticsStockholm UniversityStockholmSweden

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