Abstract
Consider a series whose terms are random variables; denote the values taken by y n (their number is finite or, possibly, countable) by and the corresponding probabilities by Further, denote by the expectation of y n , and by the expectation of the square of the deviation y n —a n
*
Über Konvergenz von Reihen, deren Glieder durch den Zufall bestimmt werden’, Mat. Sb. 32 (1925), 668-677.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Notes
Math. Ann.87 (1922), 135.
Clearly, this statement is the same as that stated in the introduction. General considerations of this kind of relation can be found in Steinhaus’s work (Fund. Math. 4 (1923), 286-310).
See footnote 1.
The uniform boundedness of the y n clearly implies that of the a n and consequently that of the φ;n(x).
This means that there is a certain relation between u n and y n.
Editor information
Rights and permissions
Copyright information
© 1992 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Khinchin, A.Y. (1992). On Convergence of Series Whose Terms are Determined by Random Events. In: Shiryayev, A.N. (eds) Selected Works of A. N. Kolmogorov. Mathematics and Its Applications (Soviet Series), vol 26. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2260-3_1
Download citation
DOI: https://doi.org/10.1007/978-94-011-2260-3_1
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5003-6
Online ISBN: 978-94-011-2260-3
eBook Packages: Springer Book Archive