Abstract
This chapter is devoted to further topics in the theory of stochastic processes and of their applications. We start with a different, weaker, definition of a stochastic process, useful in the study of stationary processes.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Bibliography
G.I. Barenblatt, Scaling, Cambridge University Press, Cambridge, 2004.
G.I. Barenblatt and A.J. Chorin, A mathematical model for the scaling of turbulence, Proc. Natl. Acad. Sci. USA, 101 (2004), pp. 15,023–15,026.
A.J. Chorin, Vorticity and Turbulence, Springer-Verlag, New York, 1994.
A.J. Chorin and P. Krause, Dimensional reduction for a Bayesian filter, Proc. Natl. Acad. Sci. USA, 101 (2004), pp. 15,013–15,017.
C.K. Chui and G. Chen, Kalman Filtering, Springer-Verlag, Berlin, 1987.
A. Doucet, N. de Freitas, and N. Gordon, Sequential Monte-Carlo Methods in Practice, Springer-Verlag, New York, 2001.
B. Efron, The Jacknife, the Bootstrap, and Other Resampling Plans, CBMS-NSF Regional Conference Series, SIAM, Philadelphia, 1982.
M. Ghil and P. Melanotte-Rizzoli, Data assimilation in meteorology and oceanography, Adv. Geophys., 53 (1991), pp. 141–256.
I. Gikhman and A. Skorokhod, Introduction to the Theory of Random Processes, Saunders, Philadelphia, 1965.
P. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Springer-Verlag, Berlin, 1992.
R. Kraichnan, Dynamics of nonlinear stochastic systems, J. Math. Phys. 2 (1961), pp. 124–148.
R. Miller, Introduction to the Kalman Filter, Seminars on Data Assimilation, European Center for Medium-Range Weather Forecasts, Reading, UK (1997), pp. 47–60.
A. Yaglom, An Introduction to the Theory of Stationary Random Functions, Dover, New York, 1962.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2009 Springer-Verlag New York
About this chapter
Cite this chapter
Chorin, A.J., Hald, O.H. (2009). Stationary Stochastic Processes. In: Stochastic Tools in Mathematics and Science. Surveys and Tutorials in the Applied Mathematical Sciences, vol 1. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-1002-8_4
Download citation
DOI: https://doi.org/10.1007/978-1-4419-1002-8_4
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-1001-1
Online ISBN: 978-1-4419-1002-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)