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Time Change, Volatility, and Turbulence

In: Mathematical Control Theory and Finance

Author

Listed:
  • Ole E. Barndorff-Nielsen

    (University of Aarhus, The T.N. Thiele Centre for Applied Mathematics in Natural Science, Department of Mathematical Sciences)

  • Jürgen Schmiegel

    (University of Aarhus, The T.N. Thiele Centre for Applied Mathematics in Natural Science, Department of Mathematical Sciences)

Abstract

Summary A concept of volatility modulated Volterra processes is introduced. Apart from some brief discussion of generalities, the paper focusses on the special case of backward moving average processes driven by Brownian motion. In this framework, a review is given of some recent modelling of turbulent velocities and associated questions of time change and universality. A discussion of similarities and differences to the dynamics of financial price processes is included.

Suggested Citation

  • Ole E. Barndorff-Nielsen & Jürgen Schmiegel, 2008. "Time Change, Volatility, and Turbulence," Springer Books, in: Andrey Sarychev & Albert Shiryaev & Manuel Guerra & Maria do Rosário Grossinho (ed.), Mathematical Control Theory and Finance, pages 29-53, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-69532-5_3
    DOI: 10.1007/978-3-540-69532-5_3
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