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 300
... hence it is necessary . -― As in the preceding proof this condition ensures the stochastic bounded- ness of { S " } . Thus if { S , - b } is stochastically bounded , the same is true of { S , ' b1 } , and hence also of the row sums of ...
... hence it is necessary . -― As in the preceding proof this condition ensures the stochastic bounded- ness of { S " } . Thus if { S , - b } is stochastically bounded , the same is true of { S , ' b1 } , and hence also of the row sums of ...
Page 384
... hence y = 0. Put_z ( t ) = d ( I + t ) where I is a fixed finite interval . Then z is a bounded solution of the convolution equation z = Fz and hence z ( t ) = const by the lemma of XI , 2 . But z vanishes identically for t near - ∞o and ...
... hence y = 0. Put_z ( t ) = d ( I + t ) where I is a fixed finite interval . Then z is a bounded solution of the convolution equation z = Fz and hence z ( t ) = const by the lemma of XI , 2 . But z vanishes identically for t near - ∞o and ...
Page 467
... hence unique . In matrix notation ( 9.4 ) reads uP ( t ) = u and has the ordinary Laplace transform ( 9.6 ) κλΠ ( λ ) = น . If a vector u satisfies ( 9.6 ) for some particular value λ > 0 the resolvent equation ( 7.15 ) entails the ...
... hence unique . In matrix notation ( 9.4 ) reads uP ( t ) = u and has the ordinary Laplace transform ( 9.6 ) κλΠ ( λ ) = น . If a vector u satisfies ( 9.6 ) for some particular value λ > 0 the resolvent equation ( 7.15 ) entails the ...
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