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

Alexander Saichev (), Yannick Malevergne and Didier Sornette ()
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Alexander Saichev: Nizhni Novgorod State University
Didier Sornette: EMLYON Business School – Cefra

Chapter Chapter 2 in Theory of Zipf's Law and Beyond, 2010, pp 9-18 from Springer

Abstract: 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.

Keywords: Balance Condition; Wiener Process; Geometric Brownian Motion; Stochastic Behavior; Balance Growth Path (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:lnechp:978-3-642-02946-2_2

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DOI: 10.1007/978-3-642-02946-2_2

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