The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Wiener Process

  • A. G. Malliaris
Reference work entry
DOI: https://doi.org/10.1057/978-1-349-95189-5_1539

Abstract

Brownian motion is the most renowned, and historically the first stochastic process that was thoroughly investigated. It is named after the English botanist, Robert Brown, who in 1827 observed that small particles immersed in a liquid exhibited ceaseless irregular motion. Brown himself mentions several precursors starting at the beginning with Leeuwenhoek (1632–1723). In 1905 Einstein, unaware of the existence of earlier investigations about Brownian motion, obtained a mathematical derivation of this process from the laws of physics. The theory of Brownian motion was further developed by several distinguished mathematical physicists until Norbert Wiener gave it a rigorous mathematical formulation in his 1918 dissertation and in later papers. This is why the Brownian motion is also called the Wiener process. For a brief history of the scientific developments of the process see Nelson (Dynamical theories of Brownian motion. Princeton: Princeton University Press, 1967).

Keywords

Bachelier, L. Brownian motion: see Wiener process Geometric Wiener process Stochastic calculus Uncertainty Wiener process 

JEL Classifications

C0 
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Bibliography

  1. Billingsley, P. 1999. Probability and measure. 3rd ed. New York: Wiley.Google Scholar
  2. Chang, F.R. 2004. Stochastic optimization in continuous time. New York: Cambridge University Press.CrossRefGoogle Scholar
  3. Cootner, P.H. 1964. The random character of stock market prices. Cambridge, MA: MIT Press.Google Scholar
  4. Knight, F.B. 1981. Essentials of Brownian motion and diffusion, Mathematical surveys, number 18. Providence: American Mathematical Society.CrossRefGoogle Scholar
  5. Malliaris, A.G., and W.A. Brock. 1982. Stochastic methods in economics and finance. Amsterdam: North-Holland Publishing Company.Google Scholar
  6. Merton, R.C. 1990. Continuous-time finance. Malden: Blackwell.Google Scholar
  7. Nelson, E. 1967. Dynamical theories of Brownian motion. Princeton: Princeton University Press.Google Scholar

Copyright information

© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • A. G. Malliaris
    • 1
  1. 1.