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Continuous Gibrat’s Law and Gabaix’s Derivation of Zipf’s Law

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 this chapter, we describe in detail the continuous version of Gibrat’s law and explain its close connection with the geometric Brownian motion (GBM), underlying any scale independent stochastic process. Due to the importance of the GBM for many economical, physical, biological and sociological applications, we focus our attention on the basic key properties of GBM. Some more subtle statistical properties of the GBM necessary for a deep understanding of the behavior of its realizations and, ultimately, the corresponding power distributions, are discussed in the following chapters. Although the GBM adequately simulates stochastic processes occurring in various scientific fields, here and for the remaining of the book, we use the terminology of firm’s asset values.

Suggested Citation

  • Alexander Saichev & Yannick Malevergne & Didier Sornette, 2010. "Continuous Gibrat’s Law and Gabaix’s Derivation of Zipf’s Law," Lecture Notes in Economics and Mathematical Systems, in: Theory of Zipf's Law and Beyond, chapter 0, pages 9-18, Springer.
    • Handle: RePEc:spr:lnechp:978-3-642-02946-2_2
    DOI: 10.1007/978-3-642-02946-2_2
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