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 58
... Random Walks In discussing random walks one pretends usually that the successive jumps occur at epochs 1 , 2 , . . . . It should be clear , however , that this convention merely lends color to the description and that the model is ...
... Random Walks In discussing random walks one pretends usually that the successive jumps occur at epochs 1 , 2 , . . . . It should be clear , however , that this convention merely lends color to the description and that the model is ...
Page 190
... random variables , but possibly defective . With these preparations we are now in a position to introduce the important random variables on which much of the analysis of random walks will be based . Definition . The kth ( ascending ) ...
... random variables , but possibly defective . With these preparations we are now in a position to introduce the important random variables on which much of the analysis of random walks will be based . Definition . The kth ( ascending ) ...
Page 375
... random walk following the first ladder epoch is a probabilistic replica of the whole random walk . Its first ladder point is the second point of the whole random walk with the property that ( 1.6 ) 1 Sn > So , ... , Sn > Sn - 1 ; it ...
... random walk following the first ladder epoch is a probabilistic replica of the whole random walk . Its first ladder point is the second point of the whole random walk with the property that ( 1.6 ) 1 Sn > So , ... , Sn > Sn - 1 ; it ...
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