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Useful Properties of Realizations of the Geometric Brownian Motion

In: Theory of Zipf's Law and Beyond

Author

Listed:
  • Alexander Saichev

    (Nizhni Novgorod State University)

  • Yannick Malevergne

    (University of Saint-Etienne
    Technology and Economics)

  • Didier Sornette

    (EMLYON Business School – Cefra)

Abstract

In the previous chapter, we introduced the mean density of firm’s asset values (3.18), taking into account the flow of firm’s births {t i }. We provided a preliminary analysis of the properties of the mean density of firm sizes. In order to understand more deeply the roots of the power laws (3.24) and (3.25), and at the same time the basis of Zipf’s law (3.27) and (3.28), we discuss in detail in this chapter the statistical properties of the realizations of the GBM (2.11).

Suggested Citation

  • Alexander Saichev & Yannick Malevergne & Didier Sornette, 2010. "Useful Properties of Realizations of the Geometric Brownian Motion," Lecture Notes in Economics and Mathematical Systems, in: Theory of Zipf's Law and Beyond, chapter 0, pages 41-57, Springer.
    • Handle: RePEc:spr:lnechp:978-3-642-02946-2_4
    DOI: 10.1007/978-3-642-02946-2_4
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