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 286
... group ( 2.8 ) is generated by a ( F1 ) and we shall indicate its elements by the abbreviation Q ( t ) = ea ( −1 ) t ̧ a ( b ) Translations . Denote by T , the distribution concentrated at a and by I ... SEMI - GROUPS Convolution Semi-groups.
... group ( 2.8 ) is generated by a ( F1 ) and we shall indicate its elements by the abbreviation Q ( t ) = ea ( −1 ) t ̧ a ( b ) Translations . Denote by T , the distribution concentrated at a and by I ... SEMI - GROUPS Convolution Semi-groups.
Page 296
William Feller. * 5a . Discontinuous Semi - groups It is natural to ask whether there exist discontinuous semi - groups . The question is of no practical importance but the answer has some curiousity value : Every convolution semi - group ...
William Feller. * 5a . Discontinuous Semi - groups It is natural to ask whether there exist discontinuous semi - groups . The question is of no practical importance but the answer has some curiousity value : Every convolution semi - group ...
Page 340
William Feller. From now on we concentrate on semi - groups of contraction operators and impose a regularity condition on them . Denote again by 1 the identity operator , 1u = u . Definition . A semi - group of contraction operators Q ...
William Feller. From now on we concentrate on semi - groups of contraction operators and impose a regularity condition on them . Denote again by 1 the identity operator , 1u = u . Definition . A semi - group of contraction operators Q ...
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