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 322
... derived formally from ( 4.2 ) – ( 4.4 ) , but we shall not discuss under what conditions there exist solutions to ... derive the backward equation ( 4.6 ) we start from the identity ( 4.7 ) u ( s + t , x ) = = √2 , ( x , Q ̧ ( x , dy ) ...
... derived formally from ( 4.2 ) – ( 4.4 ) , but we shall not discuss under what conditions there exist solutions to ... derive the backward equation ( 4.6 ) we start from the identity ( 4.7 ) u ( s + t , x ) = = √2 , ( x , Q ̧ ( x , dy ) ...
Page 373
... derived anew and supplemented in chapter XVIII by Fourier methods . ( Other aspects of random walks were covered in VI , 10 . ) In the main our attention will be restricted to two central topics . First , it will be shown that the ...
... derived anew and supplemented in chapter XVIII by Fourier methods . ( Other aspects of random walks were covered in VI , 10 . ) In the main our attention will be restricted to two central topics . First , it will be shown that the ...
Page 444
... derive from ( 2.3 ) an explicit formula for the solution . For reasons that will become apparent we switch to the tail 1 V ( t ) ... derived by different methods in example XI , ( 7.a ) . The problem is to find a probability distribution R ...
... derive from ( 2.3 ) an explicit formula for the solution . For reasons that will become apparent we switch to the tail 1 V ( t ) ... derived by different methods in example XI , ( 7.a ) . The problem is to find a probability distribution R ...
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