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Unconditional limit theorems from conditional limit theorems
Journal of Nonparametric Statistics, 1997The method of proof developed here may be used to obtain unconditional limit theorems from conditional limit theorems in a variety of settings. It is known that given two samples with the same arbitrary nondegenerate common distribution function, the conditional distribution of the sum of the tied midranks of one sample within the pooled ordered sample,
Mark Finkelstein, Howard G. Tucker
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Advances in Applied Probability, 1976
Let be an adapted sequence of integrable random variables on the probability space . Let us set .The following result can be immediately derived from Brown [2]:
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Let be an adapted sequence of integrable random variables on the probability space . Let us set .The following result can be immediately derived from Brown [2]:
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Theory of Probability & Its Applications, 1976
Limit theorems are proved by using certain pseudometrics as distances between distributions in the scheme of summation of series of independent random variables with values in a separable Hilbert space.
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Limit theorems are proved by using certain pseudometrics as distances between distributions in the scheme of summation of series of independent random variables with values in a separable Hilbert space.
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2008
At the end of the 17th century, the mathematician Abraham de Moivre first used the normal distribution as an approximation for the percentage of successes in a large number of experiments. Later on, Laplace generalized his results, but it took 20th century mathematics to give an exact and complete description of this subject. So let me now describe the
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At the end of the 17th century, the mathematician Abraham de Moivre first used the normal distribution as an approximation for the percentage of successes in a large number of experiments. Later on, Laplace generalized his results, but it took 20th century mathematics to give an exact and complete description of this subject. So let me now describe the
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Functional Central Limit Theorems
2008Central limit theorems guarantee that the distributions of properly normalized sums of certain random variables are approximately normal. In many cases, however, a more detailed analysis is necessary. When testing for structural constancy in models, we might be interested in the temporal evolution of our sums.
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2017
In this chapter we introduce selected limit theorems on fuzzy quantum space, namely Egorov’s theorem, Central limit theorem, Weak and strong law of large numbers, and extreme value theorems for fuzzy quantum space. We also study here the Ergodic theory for fuzzy quantum space and Ergodic theorems and Poincaré recurrence theorems for fuzzy quantum ...
Renáta Bartková +2 more
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In this chapter we introduce selected limit theorems on fuzzy quantum space, namely Egorov’s theorem, Central limit theorem, Weak and strong law of large numbers, and extreme value theorems for fuzzy quantum space. We also study here the Ergodic theory for fuzzy quantum space and Ergodic theorems and Poincaré recurrence theorems for fuzzy quantum ...
Renáta Bartková +2 more
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