Abstract
The goals of this chapter are to: • Extend the notion of uniformity, • Study the metrization of weak convergence, • Describe the notion of vague convergence, • Consider the question of its metrization.
Keywords
- Vague Convergence
- Weak Convergence
- Kantorovich Metric
- Bounded Borel Subset
- Nonnegative Continuous Function
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
References
Billingsley P (1999) Convergence of probability measures, 2nd edn. Wiley, New York
Fortet R, B Mourier (1953) Convergence de la réparation empirique vers la répétition theorétique. Ann Sci Ecole Norm 70:267–285
Hennequin PL, Tortrat A (1965) Théorie des probabilités et quelques applications. Masson, Paris
Kallenberg O (1975) Random measures. Akademie, Berlin
Kerstan J, Matthes K, Mecke J (1978) Infinitely divisible point processes. Wiley, New York
Prokhorov YuV (1956) Convergence of random processes and limit theorems in probability theory. Theor Prob Appl 1:157–214
Ranga RR (1962) Relations between weak and uniform convergence of measures with applications. Ann Math Statist 33:659–680
Szasz D (1975) On a metrization of the vague convergence. Studio Sci Math Hungarica 9:219–222
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Rachev, S.T., Klebanov, L.B., Stoyanov, S.V., Fabozzi, F.J. (2013). Uniformity in Weak and Vague Convergence. In: The Methods of Distances in the Theory of Probability and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4869-3_11
Download citation
DOI: https://doi.org/10.1007/978-1-4614-4869-3_11
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-4868-6
Online ISBN: 978-1-4614-4869-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)