An Introduction to Probability Theory and Its Applications, Volume 2 |
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Page 184
... renewal argument " to be used time and again for the derivation of various distributions and expectations . Two obvious generalizations of a renewal process are useful . First we consider terminating processes where the process can stop ...
... renewal argument " to be used time and again for the derivation of various distributions and expectations . Two obvious generalizations of a renewal process are useful . First we consider terminating processes where the process can stop ...
Page 186
... renewal processes with arbitrary interarrival times.16 We turn to problems of a fairly general character connected with renewal processes . The distribution underlying the process is again denoted by F. We begin with what could be ...
... renewal processes with arbitrary interarrival times.16 We turn to problems of a fairly general character connected with renewal processes . The distribution underlying the process is again denoted by F. We begin with what could be ...
Page 216
... renewal epochs are of the form T1 + ··· + T2 + 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 ...
... renewal epochs are of the form T1 + ··· + T2 + 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 ...
Contents
CHAPTER | 1 |
SPECIAL DENSITIES RANDOMIZATION | 41 |
3 Related Distributions of Statistics | 47 |
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 derived distribution concentrated distribution F distribution function equals example exists exponential distribution F{dx F{dy finite interval fixed follows formula Fourier given hence implies independent random variables inequality infinitely divisible integral Laplace transform law of large left side lemma Let F limit distribution Markov martingale measure mutually independent normal distribution notation o-algebra 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