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 31
... vector is 2 + 2 cos . Here is the angle between the two random vectors , and hence cos C is uni- formly distributed ... vector in R3 is meant a vector drawn in a random direction with a length L which is a random variable independent of ...
... vector is 2 + 2 cos . Here is the angle between the two random vectors , and hence cos C is uni- formly distributed ... vector in R3 is meant a vector drawn in a random direction with a length L which is a random variable independent of ...
Page 461
... vector § ( 2 ) in ( 7.18 ) represents the maximal vector satisfying ( 7.19 ) . We have thus Theorem 3. The row defects of the minimal solution are represented by the well - defined maximal vector § ( 2 ) satisfying ( 7.19 ) . ( 00 ) ...
... vector § ( 2 ) in ( 7.18 ) represents the maximal vector satisfying ( 7.19 ) . We have thus Theorem 3. The row defects of the minimal solution are represented by the well - defined maximal vector § ( 2 ) satisfying ( 7.19 ) . ( 00 ) ...
Page 467
... vector u satisfies ( 9.6 ) for some particular value λ > 0 the resolvent equation ( 7.15 ) entails the truth of ... vector satisfying ( 9.7 ) it follows by induction from ( 7.12 ) that uλII ( " ) ( λ ) ≤ u for all n , and hence uλ ( 2 ) ...
... vector u satisfies ( 9.6 ) for some particular value λ > 0 the resolvent equation ( 7.15 ) entails the truth of ... vector satisfying ( 9.7 ) it follows by induction from ( 7.12 ) that uλII ( " ) ( λ ) ≤ u for all n , and hence uλ ( 2 ) ...
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 |
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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