An Introduction to Probability Theory and Its Applications, Volume 2Wiley, 1950 - Probabilities Vol. 2 has series: Wiley series in probability and mathematical statistics. Bibliographical footnotes. "Some books on cagnate subjects": v. 2, p. 615-616. |
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Page 88
... sequences in terms of a given sequence { Z } will be described . They are in constant use in time series analysis and may serve as an exercise in routine manipulations . Examples . ( a ) Generalized moving average processes . With ...
... sequences in terms of a given sequence { Z } will be described . They are in constant use in time series analysis and may serve as an exercise in routine manipulations . Examples . ( a ) Generalized moving average processes . With ...
Page 261
... sequence of points . Every sequence { u } of numerical functions contains a subsequence un ung ... that con- verges at all points a , ( possibly to ∞ ) . Vk Proof . We use G. Cantor's “ diagonal method . " It is possible to find a sequence ...
... sequence of points . Every sequence { u } of numerical functions contains a subsequence un ung ... that con- verges at all points a , ( possibly to ∞ ) . Vk Proof . We use G. Cantor's “ diagonal method . " It is possible to find a sequence ...
Page 263
... sequence G1 , G2 , .... Thus there exists a sequence { G } of distributions with zero expectations and finite variances such that every distribution F is the limit of some subsequence { G } ( d ) The proof that F " → 0 outlined in ...
... sequence G1 , G2 , .... Thus there exists a sequence { G } of distributions with zero expectations and finite variances such that every distribution F is the limit of some subsequence { G } ( d ) The proof that F " → 0 outlined in ...
Contents
CHAPTER | 1 |
SPECIAL DENSITIES RANDOMIZATION | 44 |
PROBABILITY MEASURES AND SPACES | 101 |
Copyright | |
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An Introduction to Probability Theory and Its Applications, Volume 2 William Feller Limited preview - 1991 |
Common terms and phrases
a₁ applies arbitrary argument assume asymptotic atoms backward equation Baire functions Borel sets bounded central limit theorem characteristic function common distribution compound Poisson condition consider constant continuous function convergence convolution defined definition denote density derived distribution F distribution function equals example exists exponential distribution F{dx finite interval fixed follows formula given hence implies independent random variables inequality infinitely divisible integral integrand Laplace transform law of large left side lemma Let F limit distribution Markov martingale measure mutually independent normal distribution notation o-algebra obvious operator parameter Poisson process positive probabilistic probability distribution problem proof prove random walk renewal epochs renewal equation renewal process S₁ sample space satisfies semi-group sequence shows solution stable distributions stochastic stochastic kernel symmetric T₁ tends theory transition probabilities uniformly unique variance vector X₁ Y₁ zero expectation