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Capacités et processus stochastiques

  • Claude Dellacherie
Book

Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge book series (MATHE2, volume 67)

Table of contents

  1. Front Matter
    Pages I-IX
  2. Introduction

    1. Claude Dellacherie
      Pages 1-3
  3. Théorie de l’approximation par en dessous

    1. Claude Dellacherie
      Pages 5-21
    2. Claude Dellacherie
      Pages 22-42
    3. Back Matter
      Pages 43-44
  4. Théorie générale des processus

    1. Claude Dellacherie
      Pages 45-65
    2. Claude Dellacherie
      Pages 66-93
    3. Claude Dellacherie
      Pages 94-124
    4. Claude Dellacherie
      Pages 125-143
    5. Back Matter
      Pages 144-146
  5. Back Matter
    Pages 147-158

About this book

Introduction

From the reviews (Zentrallblatt MATH):

"This book consists of two sections. The first section (A) is dealing with sets, capacities and measures of sets, giving elementary but deep theorems about approximation of measures and capacities for instance by compact sets. Besides concepts such as "paving capacity" and "capacibility" several modern and quite new concepts such as "capacitance", "mosaic", "envelope", and "scarper" ("rabotage") are introduces in order to describe refinements of the structure of classes of sets. Using these concepts the author proves in a new way know theorems such as Choquet's theorem in abstract form and he also gives new theorems for instance theorems about analytic sets.

The second section (B) presents a general theory of stochastic processes but is mainly concerned with fundaments. It gives a far-reaching theory of stopping times and q-fields belonging to stopping times and classifications of stopping times and q-fields. This theory is then applied to stochastic processes, particularly to processes with realizations that are increasing functions. This book is well-fitted for researchers, who need a thorough knowledge of stochastic processes."

Keywords

paving capacity capacibility capacitance mosaic envelope scraper Choquet's theorem stopping times martingale theory

Authors and affiliations

  • Claude Dellacherie
    • 1
  1. 1.Institut de MathématiqueUniversité de StrasbourgFrance

Bibliographic information

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