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 184
William Feller. expected number of renewal epochs in 0 , x is U ( x - y ) . Summing over y we get ( 6.5 ) . This is the standard “ renewal argument " to be used time and again for the derivation of various distributions and expectations ...
William Feller. expected number of renewal epochs in 0 , x is U ( x - y ) . Summing over y we get ( 6.5 ) . This is the standard “ renewal argument " to be used time and again for the derivation of various distributions and expectations ...
Page 216
... renewal epochs are of the form T1 + + T + Y where the last variable has a different distribution . Show that the distribution V of the duration of the process satisfies the renewal equation ( * ) V = qFo + F ☆ V ... ( F ( ∞ ) = 1 q ) ...
... renewal epochs are of the form T1 + + T + Y where the last variable has a different distribution . Show that the distribution V of the duration of the process satisfies the renewal equation ( * ) V = qFo + F ☆ V ... ( F ( ∞ ) = 1 q ) ...
Page 361
... renewal epochs within 0 , ; this time , however , the expected number of renewal epochs ever occurring is finite , namely ( 6.2 ) 1 U ( ∞ ) = 1 Loo The probability that the nth renewal epoch S , is the last and ≤ x equals ( 1 - L ...
... renewal epochs within 0 , ; this time , however , the expected number of renewal epochs ever occurring is finite , namely ( 6.2 ) 1 U ( ∞ ) = 1 Loo The probability that the nth renewal epoch S , is the last and ≤ x equals ( 1 - L ...
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