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 91
... satisfies ( 7.13 ) . It follows that we can add to the solution of example ( b ) an arbitrary stationary sequence satisfying ( 7.13 ) , and the latter will represent the contribution of the infinitely remote past . A remark concerning ...
... satisfies ( 7.13 ) . It follows that we can add to the solution of example ( b ) an arbitrary stationary sequence satisfying ( 7.13 ) , and the latter will represent the contribution of the infinitely remote past . A remark concerning ...
Page 305
... satisfies the conditions of the theorem for some fixed values of the parameters . It follows from ( 8.6 ) that for « > 1 a finite expectation exists and in this case we suppose that F is centered to zero expectation . Letting b ...
... satisfies the conditions of the theorem for some fixed values of the parameters . It follows from ( 8.6 ) that for « > 1 a finite expectation exists and in this case we suppose that F is centered to zero expectation . Letting b ...
Page 460
... satisfies the forward equation . Repeating the above argument it is seen that again any non - negative solution satisfies ( 7.11 ) . We have thus proved Theorem 1. There exists a matrix II ( ∞ ) ( λ ) ≥ 0 with row sums ≤2-1 ...
... satisfies the forward equation . Repeating the above argument it is seen that again any non - negative solution satisfies ( 7.11 ) . We have thus proved Theorem 1. There exists a matrix II ( ∞ ) ( λ ) ≥ 0 with row sums ≤2-1 ...
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