Convergence of integrated superpositions of Ornstein-Uhlenbeck processes to fractional Brownian motion

Abstract

Superpositions of Ornstein-Uhlenbeck processes provide convenient ways to build stationary processes with given marginal distributions and long range dependence. After reviewing some of the basic features, we present several examples of processes with non-Gaussian marginal distributions. Our main results concern asymptotic properties of sums and partial sums of these processes and their polynomial functions. Further, we discuss some applications to estimation.

Keywords:

• Ornstein Uhlenbeck process
• Superposition
• Fractional Brownian motion
• Long range dependence
• Self-decomposability

AMS Subject Classification:

• 60F05
• 60F17
• 62F12
• 62M10

Notes

‡Email: [email protected]

^¶ Work partially supported by EPSRC grant RCMT091

^∥ Work partially supported by Cofin MIUR 200

Additional information

Notes on contributors

Nikolai Leonenko

‡ ‡Email: [email protected] ¶ ¶ Work partially supported by EPSRC grant RCMT091

Emanuele Taufer

∥ ∥ Work partially supported by Cofin MIUR 200