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Random element

About: Random element is a research topic. Over the lifetime, 4620 publications have been published within this topic receiving 156337 citations.


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Book
01 Jan 1965
TL;DR: This chapter discusses the concept of a Random Variable, the meaning of Probability, and the axioms of probability in terms of Markov Chains and Queueing Theory.
Abstract: Part 1 Probability and Random Variables 1 The Meaning of Probability 2 The Axioms of Probability 3 Repeated Trials 4 The Concept of a Random Variable 5 Functions of One Random Variable 6 Two Random Variables 7 Sequences of Random Variables 8 Statistics Part 2 Stochastic Processes 9 General Concepts 10 Random Walk and Other Applications 11 Spectral Representation 12 Spectral Estimation 13 Mean Square Estimation 14 Entropy 15 Markov Chains 16 Markov Processes and Queueing Theory

13,886 citations

Book ChapterDOI
TL;DR: In this article, upper bounds for the probability that the sum S of n independent random variables exceeds its mean ES by a positive number nt are derived for certain sums of dependent random variables such as U statistics.
Abstract: Upper bounds are derived for the probability that the sum S of n independent random variables exceeds its mean ES by a positive number nt. It is assumed that the range of each summand of S is bounded or bounded above. The bounds for Pr {S – ES ≥ nt} depend only on the endpoints of the ranges of the summands and the mean, or the mean and the variance of S. These results are then used to obtain analogous inequalities for certain sums of dependent random variables such as U statistics and the sum of a random sample without replacement from a finite population.

8,655 citations

Book
18 Jul 1996
TL;DR: Random Closed Sets I--The Boolean Model. Random Closed Sets II--The General Case.
Abstract: Mathematical Foundation. Point Processes I--The Poisson Point Process. Random Closed Sets I--The Boolean Model. Point Processes II--General Theory. Point Processes III--Construction of Models. Random Closed Sets II--The General Case. Random Measures. Random Processes of Geometrical Objects. Fibre and Surface Processes. Random Tessellations. Stereology. References. Indexes.

4,079 citations

Book
01 Jan 1982
TL;DR: In this article, the authors present a survey of the history and varieties of probability for the laws of chance and their application in the context of Markov chains convergence of random variables.
Abstract: Events and their probabilities random variables and their distributions discrete random variables continuous random variables generating functions and their applications Markov chains convergence of random variables random processes stationary processes renewals queues Martingales diffusion processes. Appendices: Foundations and notations history and varieties of probability John Arburthnot's preface to "Of the Laws of Chance" (1692).

2,819 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20239
202222
20216
202013
201915
201823