Abstract
In this chapter we review a number of basic probabilistic tools that will needed for the study of stochastic processes in the subsequent chapters. We refer to Devore (Probability and Statistics for Engineering and the Sciences. Duxbury Press, sixth edition, 2003), Jacod and Protter (Probability Essentials. Springer, 2000), and Pitman (Probability. Springer, 1999) for additional probability material.
This is a preview of subscription content, log in via an institution to check access.
Notes
- 1.
Measurability of subsets of \(\mathbb{R}\) refers to Borel measurability, a concept which will not be defined in this text.
- 2.
Here \(G_{X}' (1^{-})\) denotes the derivative on the left at the point 1.
Bibliography
Devore, J.L.: Probability and Statistics for Engineering and the Sciences, 6th edn. Duxbury Press, N. Scituate (2003)
Jacod, J., Protter, P.: Probability Essentials. Springer, Berlin (2000)
Kallenberg, O.: Foundations of Modern Probability, 2nd edn. Probability and Its Applications. Springer, New York (2002)
Lukacs, E.: Characteristic Functions, revised and enlarged 2nd edn. Hafner Publishing, New York (1970)
Pitman, J.: Probability. Springer, Berlin (1999)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media Singapore
About this chapter
Cite this chapter
Privault, N. (2013). Probability Background. In: Understanding Markov Chains. Springer Undergraduate Mathematics Series. Springer, Singapore. https://doi.org/10.1007/978-981-4451-51-2_2
Download citation
DOI: https://doi.org/10.1007/978-981-4451-51-2_2
Publisher Name: Springer, Singapore
Print ISBN: 978-981-4451-50-5
Online ISBN: 978-981-4451-51-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)