Convergence of Probability MeasuresJohn Wiley & Sons, 25 giu 2013 - 304 pagine A new look at weak-convergence methods in metric spaces-from a master of probability theory In this new edition, Patrick Billingsley updates his classic work Convergence of Probability Measures to reflect developments of the past thirty years. Widely known for his straightforward approach and reader-friendly style, Dr. Billingsley presents a clear, precise, up-to-date account of probability limit theory in metric spaces. He incorporates many examples and applications that illustrate the power and utility of this theory in a range of disciplines-from analysis and number theory to statistics, engineering, economics, and population biology. With an emphasis on the simplicity of the mathematics and smooth transitions between topics, the Second Edition boasts major revisions of the sections on dependent random variables as well as new sections on relative measure, on lacunary trigonometric series, and on the Poisson-Dirichlet distribution as a description of the long cycles in permutations and the large divisors of integers. Assuming only standard measure-theoretic probability and metric-space topology, Convergence of Probability Measures provides statisticians and mathematicians with basic tools of probability theory as well as a springboard to the "industrial-strength" literature available today. |
Dall'interno del libro
Risultati 1-5 di 85
Pagina
... CONVERGENCE SECTION 3. CONVERGENCE IN DISTRIBUTION SECTION 4. LONG CYCLES AND LARGE DIVISORSj SECTION 5. PROHOROV'S THEOREM SECTION 6. A MISCELLANYj CHAPTER 2: THE SPACE C SECTION 7. WEAK CONVERGENCE AND TIGHTNESS IN C SECTION 8. WIENER ...
... CONVERGENCE SECTION 3. CONVERGENCE IN DISTRIBUTION SECTION 4. LONG CYCLES AND LARGE DIVISORSj SECTION 5. PROHOROV'S THEOREM SECTION 6. A MISCELLANYj CHAPTER 2: THE SPACE C SECTION 7. WEAK CONVERGENCE AND TIGHTNESS IN C SECTION 8. WIENER ...
Pagina
... Convergence of probability measures / Patrick Billingsley. — 2nd ed. p.cm. — (Wiley series in probability and statistics. Probability and statistics) “Wiley-lnterscience publication.” Includes bibliographical references and indexes ...
... Convergence of probability measures / Patrick Billingsley. — 2nd ed. p.cm. — (Wiley series in probability and statistics. Probability and statistics) “Wiley-lnterscience publication.” Includes bibliographical references and indexes ...
Pagina
... convergence of distribution functions in Euclidean space—convergence, that is, at continuity points of the limit function. The past several decades have seen the creation and extensive application of a more inclusive theory of weak ...
... convergence of distribution functions in Euclidean space—convergence, that is, at continuity points of the limit function. The past several decades have seen the creation and extensive application of a more inclusive theory of weak ...
Pagina
... distribution functions Fn and F on the line that Fn converges weakly to F, which we indicate by writing Fn => F, if (3) holds at every continuity point x of F. Thus the De MoivreLaplace theorem says that (1) converges weakly to (2); ...
... distribution functions Fn and F on the line that Fn converges weakly to F, which we indicate by writing Fn => F, if (3) holds at every continuity point x of F. Thus the De MoivreLaplace theorem says that (1) converges weakly to (2); ...
Pagina
... convergence of distribution functions is tied to the real line (or to Euclidean space, at any rate), the concept of weak convergence of probability measures can be formulated for the general metric space, which is the real reason for ...
... convergence of distribution functions is tied to the real line (or to Euclidean space, at any rate), the concept of weak convergence of probability measures can be formulated for the general metric space, which is the real reason for ...
Sommario
THE SPACE C | ix |
THE SPACE D | viii |
DEPENDENT VARIABLES | xlviii |
OTHER MODES OF CONVERGENCE | lxiii |
APPENDIX_M | 16 |
INDEX | 38 |
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Analysis apply argument assume Borel o-field Borel sets Brownian motion cadlag functions central limit theorem choose compact set condition contains convergence in distribution convergence-determining class converges weakly convex countable defined denote dense density distribution function Donsker’s theorem equivalent ergodic Example exist finite finite-dimensional distributions finite-dimensional sets hence holds hypothesis image and image image image inequality infimum integral interval Lebesgue measure Lemma Let image lim sup limiting distribution linear log log mapping theorem measurable Image metric space nonnegative open sets P-continuity set partial sums permutation points polygonal positive prime divisors probability measure probability space proof of Theorem prove random element random function random variables random walk relatively compact satisfies Second Edition Section sequence Skorohod topology stationary Statistical subsequence subset Suppose supremum Theorem 3.1 tight uniformly continuous uniformly distributed values variance weak convergence Wiener measure