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 451
... equations K1 is called the Green function of ( 5.4 ) . In the present case ( 5.6 ) K1 ( x , y ) = 1 21 22 e - v2x | x - x \ In fact , it is easily verified that for bounded continuous ƒ equation ( 5.4 ) possesses a unique bounded ...
... equations K1 is called the Green function of ( 5.4 ) . In the present case ( 5.6 ) K1 ( x , y ) = 1 21 22 e - v2x | x - x \ In fact , it is easily verified that for bounded continuous ƒ equation ( 5.4 ) possesses a unique bounded ...
Page 460
... 1 ) ( 2 ) cp . This is true for n = 1. Assuming the truth of ( 7.12 ) ... equations ( 7.1 ) - ( 7.2 ) . Either all matrices P ( t ) and 2II ( ∞ ) ( 2 ) ... bounded by 1 and so it follows that II ( 2 ) is the transform of a matrix P ( t ) ...
... 1 ) ( 2 ) cp . This is true for n = 1. Assuming the truth of ( 7.12 ) ... equations ( 7.1 ) - ( 7.2 ) . Either all matrices P ( t ) and 2II ( ∞ ) ( 2 ) ... bounded by 1 and so it follows that II ( 2 ) is the transform of a matrix P ( t ) ...
Page 461
... 1 = 1 — § ( 2 ) - ( 2 + c ) § ( 2 ) = cp§ ( 2 ) , 0 ( 2 ) ≤ 1 . On the ... bounded column vectors . We saw in XIII , 10 that it holds iff the range of ... equations by the column vector 1 would seem to lead to the identity ¿ II ( 2 ) 1 1 ...
... 1 = 1 — § ( 2 ) - ( 2 + c ) § ( 2 ) = cp§ ( 2 ) , 0 ( 2 ) ≤ 1 . On the ... bounded column vectors . We saw in XIII , 10 that it holds iff the range of ... equations by the column vector 1 would seem to lead to the identity ¿ II ( 2 ) 1 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