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A Basic Course in Probability Theor

Rabi Bhattacharya Edward C. Waymire

Resumen/Descripción – provisto por la editorial

No disponible.

Palabras clave – provistas por la editorial

Probability Theory and Stochastic Processes; Measure and Integration; Analysis

Disponibilidad

Institución detectada	Año de publicación	Navegá	Descargá	Solicitá
No detectada	2007	SpringerLink

Información

Tipo de recurso:

libros

ISBN impreso

978-0-387-71938-2

ISBN electrónico

978-0-387-71939-9

Editor responsable

Springer Nature

País de edición

Reino Unido

Fecha de publicación

2007

Información sobre derechos de publicación

Cobertura temática

Matemáticas

Tabla de contenidos

Verificá que desde tu institución tengas acceso para descargar o solicitar el libro completo o alguno de sus capítulos.

doi: 10.1007/978-0-387-71939-9_1

Random Maps, Distribution, and Mathematical Expectation

In the spirit of a refresher, we begin with an overview of the measure-theoretic framework for probability. Readers for whom this is entirely new material may wish to consult the appendices for statements and proofs of basic theorems from analysis.

Palabras clave: Probability Space; Mathematical Expectation; Borel Measurable Function; Total Variation Distance; Cantelli Lemma.

Pp. 1-17

doi: 10.1007/978-0-387-71939-9_2

Independence, Conditional Expectation

Palabras clave: Independent Random Variable; Conditional Expectation; Product Measure; Closed Linear Subspace; Random Variable Versus.

Pp. 19-36

doi: 10.1007/978-0-387-71939-9_3

Martingales and Stopping Times

The notion of “martingale” has proven to be among the most powerful ideas to emerge in probability in the last century. In this section some basic foundations are presented. A more comprehensive treatment of the theory and its applications is provided in our text on stochastic processes.

Pp. 37-48

doi: 10.1007/978-0-387-71939-9_4

Classical Zero–One Laws, Laws of Large Numbers and Deviations

The term law has various meanings within probability. It is sometimes used synonymously with distribution of a random variable. However, it also may refer to an event or phenomenon that occurs in some predictable sense, as in a “law of averages.” The latter is the context of the present section.

Palabras clave: Fourth Moment; Nonnegative Random Variable; Cantelli Lemma; Tail Event; Classical Zero.

Pp. 49-58

doi: 10.1007/978-0-387-71939-9_5

Weak Convergence of Probability Measures

Pp. 59-72

doi: 10.1007/978-0-387-71939-9_6

Fourier Series, Fourier Transform, and Characteristic Functions

Palabras clave: Characteristic Function; FOURIER Series; Inversion Formula; Fourier Inversion; Continuity Theorem.

Pp. 73-98

doi: 10.1007/978-0-387-71939-9_7

Classical Central Limit Theorems

Palabras clave: Independent Random Variable; Triangular Array; Continuity Theorem; Lindeberg Condition; Independent Normal Random Variable.

Pp. 99-105

doi: 10.1007/978-0-387-71939-9_8

Laplace Transforms and Tauberian Theorem

Palabras clave: Laplace Transform; Inversion Formula; Bernstein Polynomial; TAUBERIAN Theorem; Renewal Equation.

Pp. 107-120

doi: 10.1007/978-0-387-71939-9_9

Random Series of Independent Summands

Pp. 121-127

doi: 10.1007/978-0-387-71939-9_10

Kolmogorov's Extension Theorem and Brownian Motion

Palabras clave: Brownian Motion; Polish Space; Extension Theorem; Coordinate Projection; Standard Brownian Motion.

Pp. 129-140