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Mathematical statistics --- Distribution (Probability theory) --- Sampling (Statistics) --- Stochastic processes --- Distribution (Théorie des probabilités) --- Echantillonnage (Statistique) --- Processus stochastiques --- 519.23 --- 519.22 --- 519.2 --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Random processes --- Random sampling --- Statistics of sampling --- Statistics --- Statistical analysis. Inference methods --- Statistical theory. Statistical models. Mathematical statistics in general --- Probability. Mathematical statistics --- 519.2 Probability. Mathematical statistics --- 519.22 Statistical theory. Statistical models. Mathematical statistics in general --- 519.23 Statistical analysis. Inference methods --- Distribution (Théorie des probabilités)

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Rigorous probabilistic arguments, built on the foundation of measure theory introduced seventy years ago by Kolmogorov, have invaded many fields. Students of statistics, biostatistics, econometrics, finance, and other changing disciplines now find themselves needing to absorb theory beyond what they might have learned in the typical undergraduate, calculus-based probability course. This book grew from a one-semester course offered for many years to a mixed audience of graduate and undergraduate students who have not had the luxury of taking a course in measure theory. The core of the book covers the basic topics of independence, conditioning, martingales, convergence in distribution, and Fourier transforms. In addition there are numerous sections treating topics traditionally thought of as more advanced, such as coupling and the KMT strong approximation, option pricing via the equivalent martingale measure, and the isoperimetric inequality for Gaussian processes. The book is not just a presentation of mathematical theory, but is also a discussion of why that theory takes its current form. It will be a secure starting point for anyone who needs to invoke rigorous probabilistic arguments and understand what they mean.

Measure theory --- Probabilities --- 519.2 --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra) --- 519.2 Probability. Mathematical statistics --- Probability. Mathematical statistics --- Measure theory. --- Probabilities. --- multivariaat --- waarschijnlijkheidsleer --- wiskundige statistiek

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Sampling (Statistics) --- Stochastic processes. --- Distribution (Probability theory)

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Rigorous probabilistic arguments, built on the foundation of measure theory introduced eighty years ago by Kolmogorov, have invaded many fields. Students of statistics, biostatistics, econometrics, finance, and other changing disciplines now find themselves needing to absorb theory beyond what they might have learned in the typical undergraduate, calculus-based probability course. This 2002 book grew from a one-semester course offered for many years to a mixed audience of graduate and undergraduate students who have not had the luxury of taking a course in measure theory. The core of the book covers the basic topics of independence, conditioning, martingales, convergence in distribution, and Fourier transforms. In addition there are numerous sections treating topics traditionally thought of as more advanced, such as coupling and the KMT strong approximation, option pricing via the equivalent martingale measure, and the isoperimetric inequality for Gaussian processes. The book is not just a presentation of mathematical theory, but is also a discussion of why that theory takes its current form. It will be a secure starting point for anyone who needs to invoke rigorous probabilistic arguments and understand what they mean.

Probabilities. --- Measure theory.

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Chinese literature --- Literature --- Chou Tso-jen --- Littérature chinoise --- History and criticism --- Critique et interprétation. --- Zhou, Zuoren,