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 16
Pagina
... converges weakly to F, which we indicate by writing Fn => F, if (3) holds at every ... convergence, which underlies a large class of limit theorems in probability ... class of Borel subsets of the line, are uniquely determined by the ...
... converges weakly to F, which we indicate by writing Fn => F, if (3) holds at every ... convergence, which underlies a large class of limit theorems in probability ... class of Borel subsets of the line, are uniquely determined by the ...
Pagina
... finding the limit on the left for the special case of symmetric random walk ... convergence in C to obtain a whole class of limit theorems for functions of ... convergence to another space of functions on [0, 1]— the space D[O, 1] of ...
... finding the limit on the left for the special case of symmetric random walk ... convergence in C to obtain a whole class of limit theorems for functions of ... convergence to another space of functions on [0, 1]— the space D[O, 1] of ...
Pagina
... determined by the values of PF for closed sets F. The next theorem shows ... convergence in terms of the convergence of integrals of functions, and in the ... class if two probability measures that agree on A necessarily agree also on ...
... determined by the values of PF for closed sets F. The next theorem shows ... convergence in terms of the convergence of integrals of functions, and in the ... class if two probability measures that agree on A necessarily agree also on ...
Pagina
Patrick Billingsley. the closed sets form a separating class. Recall that a class ... determines P. By Theorem 1.3, each probability measure on (RkRk) is tight ... convergence: x” —>,, x if and only if 35:' —'n 3;, for each i. Let rrk: R ...
Patrick Billingsley. the closed sets form a separating class. Recall that a class ... determines P. By Theorem 1.3, each probability measure on (RkRk) is tight ... convergence: x” —>,, x if and only if 35:' —'n 3;, for each i. Let rrk: R ...
Pagina
... class. If P is a probability measure on (R°°,R°°), its finite-dimensional distributions are the measures Pwgl on (Rk,Rk), k 2 1, and since 'f is a separating class, these measures completely determine P. Example 1.3. Let C = C[0, 1] be ...
... class. If P is a probability measure on (R°°,R°°), its finite-dimensional distributions are the measures Pwgl on (Rk,Rk), k 2 1, and since 'f is a separating class, these measures completely determine P. Example 1.3. Let C = C[0, 1] be ...
Sommario
THE SPACE C | ix |
THE SPACE D | viii |
DEPENDENT VARIABLES | xlviii |
OTHER MODES OF CONVERGENCE | lxiii |
APPENDIX_M | 16 |
INDEX | 38 |
Altre edizioni - Visualizza tutto
Parole e frasi comuni
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