Useful Properties of Realizations of the Geometric Brownian Motion

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 4 in Theory of Zipf's Law and Beyond, 2010, pp 41-57 from Springer

Abstract: 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).

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:lnechp:978-3-642-02946-2_4

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DOI: 10.1007/978-3-642-02946-2_4

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