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Preliminaries

  • K. L. Chung
  • R. J. Williams
Part of the Probability and Its Applications book series (PA)

Abstract

For each interval I in IR = (−∞, ∞) let B(I) denote the σ-field of Borel subsets of I. For each tIR+ = [0, ∞), let B t denote B([0, t]) and let B denote \(B(I{R_ + }) = {V_{t \in I{R_ + }}}\)B t — the smallest σ-field containing B t for all t in IR+. Let \(overline {I{R_ + }} = [0,\infty ]\) and \(overline B\) denote the Borel σ-field of \(overline {I{R_ + }}\) generated by B and the singleton {∞}. Let λ denote the Lebesgue measure on IR.

Keywords

Brownian Motion Poisson Process Conditional Expectation Local Martingale Optional Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston 1990

Authors and Affiliations

  • K. L. Chung
    • 1
  • R. J. Williams
    • 2
  1. 1.Department of MathematicsStanford UniversityStanfordUSA
  2. 2.Department of MathematicsUniversity of California at San DiegoLa JollaUSA

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