Abstract
The chapter begins with Sect. 11.1 establishing the Borel–Cantelli and Kolmogorov zero-one laws, and also the zero-one law for exchangeable sequences. The concepts of lower and upper functions are introduced. Section 11.2 contains the first Kolmogorov inequality and several theorems on convergence of random series. Section 11.3 presents Kolmogorov’s Strong Law of Large Numbers and Wald’s identity for stopping times. Sections 11.4 and 11.5 are devoted to the Strong Law of Large Numbers for independent non-identically distributed random variables, and to the Strong Law of Large Numbers for generalised renewal processes, respectively.
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- 1.
For more detail, see e.g. [31].
References
Shiryaev, A.N.: Probability. Springer, New York (1984)
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Borovkov, A.A. (2013). Properties of the Trajectories of Random Walks. Zero-One Laws. In: Probability Theory. Universitext. Springer, London. https://doi.org/10.1007/978-1-4471-5201-9_11
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