로그인이
필요합니다

도서를 검색해 주세요.

원하시는 결과가 없으시면 문의 주시거나 다른 검색어를 입력해보세요.

견본신청 문의
단체구매 문의
오탈자 문의

Probability Theory Ⅰ&Ⅱ(4th, 1978) 요약정보 및 구매

사용후기 0 개
지은이 M. Loeve
발행년도 1977-03-29
판수 4판
ISBN 9780387902104
도서상태 구매가능
판매가격 60,000원
포인트 0점
배송비결제 주문시 결제

상품의 재고가 부족하여 구매할 수 없습니다.

위시리스트

관련상품

  • This fourth edition contains several additions. The main ones con­cern three closely related topics: Brownian motion, functional limit distributions, and random walks. Besides the power and ingenuity of their methods and the depth and beauty of their results, their importance is fast growing in Analysis as well as in theoretical and applied Proba­bility. These additions increased the book to an unwieldy size and it had to be split into two volumes. About half of the first volume is devoted to an elementary introduction, then to mathematical foundations and basic probability concepts and tools. The second half is devoted to a detailed study of Independence which played and continues to play a central role both by itself and as a catalyst. The main additions consist of a section on convergence of probabilities on metric spaces and a chapter whose first section on domains of attraction completes the study of the Central limit problem, while the second one is devoted to random walks. About a third of the second volume is devoted to conditioning and properties of sequences of various types of dependence. The other two thirds are devoted to random functions; the last Part on Elements of random analysis is more sophisticated. The main addition consists of a chapter on Brownian motion and limit distributions. 

  • <Contents of Volume I>


    Introductory Part: Elementary Probability Theory

    I. Intuitive Background

    1. Events

    2. Random events and trials

    3. Random variables


    II. Axioms; Independence and the Bernoulli Case

    1. Axioms of the finite case

    2. Simple random variables

    3. Independence

    4. Bernoulli case

    5. Axioms for the countable case

    6. Elementary random variables

    7. Need for nonelementary random variables


    III. Dependence and Chains

    1. Conditional probabilities

    2. Asymptotically Bernoullian case

    3. Recurrence

    4. Chain dependence

    5. Types of states and asymptotic behavior

    6. Motion of the system

    7. Stationary chains

    Complements and Details


    Part One: Notions of Measure Theory

    Chapter I: Sets, Spaces, and Measures

    1. Sets, Classes, and Functions

    *2. Topological Spaces

    3. Additive Set Functions

    *4. Construction of Measures on σ-Fields

    Complements and Details


    Chapter II: Measurable Functions and Integration

    5. Measurable Functions

    6. Measure and Convergences

    7. Integration

    8. Indefinite Integrals; Iterated Integrals

    Complements and Details


    Part Two: General Concepts and Tools of Probability Theory

    Chapter III: Probability Concepts

    9. Probability Spaces and Random Variables

    10. Probability Distributions

    Complements and Details


    Chapter IV: Distribution Functions and Characteristic Functions

    11. Distribution Functions

    *12. Convergence of Probabilities on Metric Spaces

    13. Characteristic Functions and Distribution Functions

    14. Probability Laws and Types of Laws

    15. Nonnegative-definiteness; Regularity

    Complements and Details


    Part Three: Independence

    Chapter V: Sums of Independent Random Variables

    16. Concept of Independence

    17. Convergence and Stability of Sums; Centering at Expectations and Truncation

    *18. Convergence and Stability of Sums; Centering at Medians and Symmetrization

    *19. Exponential Bounds and Normed Sums

    Complements and Details


    Chapter VI: Central Limit Problem

    20. Degenerate, Normal, and Poisson Types

    21. Evolution of The Problem

    22. Central Limit Problem; The Case of Bounded Variances

    *23. Solution of The Central Limit Problem

    *24. Normed Sums

    Complements and Details


    Chapter VII: Independent Identically Distributed Summands

    25. Regular Variation and Domains of Attraction

    26. Random Walk

    Complements and Details


    Bibliography

    Index



    <Contents of Volume II>


    PART FOUR: Dependence

    Chapter VIII: Conditioning

    27. Concept of Conditioning

    28. Properties of Conditioning

    29. Regular Pr. Functions

    30. Conditional Distributions

    Complements and Details


    Chapter IX: From Independence to Dependence

    31. Central Asymptotic Problem

    32. Centerings, Martingales, and a.s. Convergence

    Complements and Details


    Chapter X: Ergodic Theorems

    33. Translation of Sequences; Basic Ergodic Theorem and Stationarity

    *34. Ergodic Theorems and Lr-Spaces

    *35. Ergodic Theorems on Banach Spaces

    Complements and Details


    Chapter XI: Second Order Properties

    36. Orthogonality

    37. Second Order Random Functions

    Complements and Details


    PART FIVE: Elements of Random Analysis

    Chapter XII: Foundations; Martingales and Decomposability

    38. Foundations

    39. Martingales

    40. Decomposability

    Complements and Details


    Chapter XIII: Brownian Motion and Limit Distributions

    41. Brownian Motion

    42. Limit Distributions

    Complements and Details


    Chapter XIV: Markov Processes

    43. Markov Dependence

    44. Time-Continuous Transition Probabilities

    45. Markov Semi-Groups

    46. Sample Continuity and Diffusion Operators

    Complements and Details


    Bibliography

    Index

  • 지은이: Michel Loeve

    Departments of Mathematics and Statistics University of California at Berkeley


    Michel Loeve is Professor Emeritus of mathematics and statistics at the University of California at Berkeley. Educated in France, he has taught in the United States for many years and held visiting professorships at Columbia University and the Universite de Paris. Dr. Loeve's interest is directed towards problems in pure and applied probability theory, a fact which is also reflected in the wide and encyclopaedic character of this book.

  • 학습자료


    등록된 학습자료가 없습니다.

    정오표


    등록된 정오표가 없습니다.

  • 상품 정보

    상품 정보 고시

  • 사용후기

    등록된 사용후기

    사용후기가 없습니다.

  • 상품문의

    등록된 상품문의

    상품문의가 없습니다.

  • 배송/교환정보

    배송정보

    cbff54c6728533e938201f4b3f80b6da_1659402509_9472.jpg

    교환/반품 정보

    cbff54c6728533e938201f4b3f80b6da_1659402593_2152.jpg