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 412
... transform of u is ∞ ( 2 ) = 2a г ( a ) . It follows that the convolution ( 2.3 ) of u and uB is given by ( 2.4 ) u ( x ) = г ( α ) г ( B ) г ( a + ẞ ) 2a + B - 1 Note that this ... LAPLACE TRANSFORMS . TAUBERIAN THEOREMS . RESOLVENTS XIII.2.
... transform of u is ∞ ( 2 ) = 2a г ( a ) . It follows that the convolution ( 2.3 ) of u and uB is given by ( 2.4 ) u ( x ) = г ( α ) г ( B ) г ( a + ẞ ) 2a + B - 1 Note that this ... LAPLACE TRANSFORMS . TAUBERIAN THEOREMS . RESOLVENTS XIII.2.
Page 448
... Laplace transform of a probability distribution F with expectation μ , the equation B ( 2 ) = q ( λ + c — cẞ ( 2 ) ) , - ( 4.1 ) λ > 0 , possesses a unique solution ẞ ; furthermore ẞ is the Laplace transform of a distribution B which is ...
... Laplace transform of a probability distribution F with expectation μ , the equation B ( 2 ) = q ( λ + c — cẞ ( 2 ) ) , - ( 4.1 ) λ > 0 , possesses a unique solution ẞ ; furthermore ẞ is the Laplace transform of a distribution B which is ...
Page 456
... Laplace transform of P , ( t ) . In this sense we have now given a new derivation for the Laplace transform of the Bessel functions In = 0 n It is typical for Laplace transforms that immediate conclusions can be drawn from the form of ...
... Laplace transform of P , ( t ) . In this sense we have now given a new derivation for the Laplace transform of the Bessel functions In = 0 n It is typical for Laplace transforms that immediate conclusions can be drawn from the form of ...
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