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 116
... definition must be suitably extended . For example , in dealing with unending sequences of trials and recurrent events in volume 1 we were given the probabilities of all events depending on finitely many trials , but this domain of ...
... definition must be suitably extended . For example , in dealing with unending sequences of trials and recurrent events in volume 1 we were given the probabilities of all events depending on finitely many trials , but this domain of ...
Page 159
... definition introduces a new notation rather than a new concept . Definition 3. A conditional expectation E ( YX ) is a function of X assuming at x the value ( 10.4 ) E ( Y | x ) = [ * ° yq ( x , dy ) provided the integral converges ...
... definition introduces a new notation rather than a new concept . Definition 3. A conditional expectation E ( YX ) is a function of X assuming at x the value ( 10.4 ) E ( Y | x ) = [ * ° yq ( x , dy ) provided the integral converges ...
Page 285
... definition of convergence consistently to arbitrary operators . - > Fiff Fu- - > Definition 2. Let A , and A be operators from C to C. We say that A converges to A , in symbols An n ( 2.3 ) for each u E C. - > A , if || A „ u — Au ...
... definition of convergence consistently to arbitrary operators . - > Fiff Fu- - > Definition 2. Let A , and A be operators from C to C. We say that A converges to A , in symbols An n ( 2.3 ) for each u E C. - > A , if || A „ u — Au ...
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