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. |
From inside the book
Results 1-3 of 83
Page 91
... solution of the problem in example ( b ) . In fact , we have found one solution of ( 7.6 ) , and the difference of two solutions satisfies ( 7.13 ) . It follows that we can add to the solution of example ( b ) an arbitrary stationary ...
... solution of the problem in example ( b ) . In fact , we have found one solution of ( 7.6 ) , and the difference of two solutions satisfies ( 7.13 ) . It follows that we can add to the solution of example ( b ) an arbitrary stationary ...
Page 319
... solution Q , is > Q ) . For this reason Q ) is called the minimal solution of the backward equation . When Qis strictly stochastic , any other solution would have to attribute to the whole space a probability ≥1 . It follows that the ...
... solution Q , is > Q ) . For this reason Q ) is called the minimal solution of the backward equation . When Qis strictly stochastic , any other solution would have to attribute to the whole space a probability ≥1 . It follows that the ...
Page 328
... solution stands for a proper probability distribution and no other solutions exist . In all other situations the minimal solution regulates the process until a boundary is reached . It corresponds to absorbing barriers , that is , it ...
... solution stands for a proper probability distribution and no other solutions exist . In all other situations the minimal solution regulates the process until a boundary is reached . It corresponds to absorbing barriers , that is , it ...
Contents
CHAPTER | 1 |
SPECIAL DENSITIES RANDOMIZATION | 44 |
PROBABILITY MEASURES AND SPACES | 101 |
Copyright | |
71 other sections not shown
Other editions - View all
An Introduction to Probability Theory and Its Applications, Volume 2 William Feller Limited preview - 1991 |
Common terms and phrases
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