Abstract
The Limit Theorems are statements about limits of sequences of sums of rv’s when the number of addenda grows to infinity.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
A function \(\varphi (u)\) is non-negative definite when, however chosen n points \(u_1,\ldots ,u_n\), the matrix \(\Vert \varphi (u_j-u_k)\Vert \) turns out to be non-negative definite, namely when, however chose n complex numbers \(z_1,\ldots ,z_n\), we always have
$$\begin{aligned} \sum _{j,k=1}^nz_j\overline{z}_k\,\varphi (u_j-u_k)\ge 0. \end{aligned}$$(4.21)
References
Shiryaev, A.N.: Probability. Springer, New York (1996)
Bouleau, N.: Probabilités de l’Ingénieur. Hermann, Paris (1986)
Feller, W.: An Introduction to Probability Theory and its Applications, vol. I-II. Wiley, New York (1968 and 1971)
Loève, M.: Probability Theory, vols. I-II. Springer, New York (1977 and 1978)
Poisson, S.D.: Recherches sur la ProbabilitÉ des Jugements en MatiÉre Criminelle et en MatiÉre Civile. Bachelier, Paris (1837)
Papoulis, A.: Probability, Random Variables and Stochastic Processes. McGraw Hill, Boston (2002)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2020 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Cufaro Petroni, N. (2020). Limit Theorems. In: Probability and Stochastic Processes for Physicists. UNITEXT for Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-48408-8_4
Download citation
DOI: https://doi.org/10.1007/978-3-030-48408-8_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-48407-1
Online ISBN: 978-3-030-48408-8
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)