Analysis and probability / Aurel Spataru.

Format:

Book

Author/Creator:

Spătaru, Aurel.

Series:

Elsevier insights.

Elsevier insights

Language:

English

Subjects (All):

Stochastic analysis.

Probabilities.

Physical Description:

1 online resource (x, 448 pages).

Edition:

1st ed.

Place of Publication:

Amsterdam ; Boston : Elsevier, 2013

London : Elsevier, 2013.

Language Note:

English

System Details:

text file

Summary:

Probability theory is a rapidly expanding field and is used in many areas of science and technology. Beginning from a basis of abstract analysis, this mathematics book develops the knowledge needed for advanced students to develop a complex understanding of probability. The first part of the book systematically presents concepts and results from analysis before embarking on the study of probability theory. The initial section will also be useful for those interested in topology, measure theory, real analysis and functional analysis. The second part of the book presents the concepts, methodo

Contents:

Analysis and Probability; Analysis and Probability; Copyright; Contents; Preface; PART ONE: ANALYSIS; Elements of Set Theory; 1 Sets and Operations on Sets; 2 Functions and Cartesian Products; 3 Equivalent Relations and Partial Orderings; References; Topological Preliminaries; 4 Construction of Some Topological Spaces; 5 General Properties of Topological Spaces; 6 Metric Spaces; Measure Spaces; 7 Measurable Spaces; 8 Measurable Functions; 9 Definitions and Properties of the Measure; 10 Extending Certain Measures; The Integral; 11 Definitions and Properties of the Integral

12 Radon-Nikodým Theorem and the Lebesgue Decomposition13 The Spaces Lp; 14 Convergence for Sequences of Measurable Functions; Measures on Product σ-Algebras; 15 The Product of a Finite Number of Measures; 16 The Product of Infinitely Many Measures; PART TWO: PROBABILITY; Elementary Notions in Probability Theory; 17 Events and Random Variables; 18 Conditioning and Independence; Distribution Functions and Characteristic Functions; 19 Distribution Functions; 20 Characteristic Functions; Reference; Probabilities on Metric Spaces; 21 Probabilities in a Metric Space

22 Topology in the Space of ProbabilitiesCentral Limit Problem; 23 Infinitely Divisible Distribution/Characteristic Functions; 24 Convergence to an Infinitely Divisible Distribution/Characteristic Function; Reference; Sums of Independent Random Variables; 25 Weak Laws of Large Numbers; 26 Series of Independent Random Variables; 27 Strong Laws of Large Numbers; 28 Laws of the Iterated Logarithm; Conditioning; 29 Conditional Expectations, Conditional Probabilities and Conditional Independence; 30 Stopping Times and Semimartingales; Ergodicity, Mixing, and Stationarity; 31 Ergodicity and Mixing

32 Stationary SequencesList of Symbols

Notes:

Description based upon print version of record

Includes bibliographical references

ISBN:

9781283970303

1283970309

9780124017276

0124017274

OCLC:

868231726