Abstract
After a historical introduction this chapter employs the explicit solution of the random walk on a one-dimensional lattice to introduce basic notions of the theory of stochastic processes to make the reader familiar with the kind of questions addressed in this area and the concepts applied for their solution. The Gaussian and the Poisson distribution are introduced as limits of the Binomial distribution.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1970)
J.-P. Bouchaud, M. Potters, Theory of Financial Risk—From Data Analysis to Risk Management (Cambridge University Press, Cambridge, 2000)
S. Chandrasekhar, Stochastic problems in physics and astronomy. Rev. Mod. Phys. 15, 1 (1943). See also in [211]
N.L. Johnson, S. Kotz, N. Balakrishnan, Continuous Univariate Distributions, vol. 1 (Wiley, New York, 1994)
N.G. van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1985)
E.W. Montroll, M.F. Shlesinger, On the wonderful world of random walks, in Nonequilibrium Phenomena II: From Stochastics to Hydrodynamics, ed. by J.L. Lebowitz, E.W. Montroll (Elsevier, Amsterdam, 1984)
K. Pearson, The history of statistics in the 17th and 18th centuries (Macmillan, London, 1978)
L.E. Reichl, A Modern Course in Statistical Physics (VCH, Weinheim, 2009)
I. Schneider (ed.), Die Entwicklung der Wahrscheinlichkeitsrechnung von den Anfängen bis 1933 (Wissenschaftliche Buchgesellschaft, Darmstadt, 1986)
V.M. Yakovenko, J. Barkley Rosser Jr., Colloquium: statistical mechanics of money, wealth, and income. Rev. Mod. Phys. 81, 1703 (2009)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Paul, W., Baschnagel, J. (2013). A First Glimpse of Stochastic Processes. In: Stochastic Processes. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00327-6_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-00327-6_1
Publisher Name: Springer, Heidelberg
Print ISBN: 978-3-319-00326-9
Online ISBN: 978-3-319-00327-6
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)