Introduction to stochastic integration: Math 642:592, Spring 2008 I. Bounded variation functions and Lebesgue-Stieltjes integrals. As a preliminary to the theory of stochastic integration, we recall the theory of Lebesgue-Stieltes

@inproceedings{2008IntroductionTS,
  title={Introduction to stochastic integration: Math 642:592, Spring 2008 I. Bounded variation functions and Lebesgue-Stieltjes integrals. As a preliminary to the theory of stochastic integration, we recall the theory of Lebesgue-Stieltes},
  author={},
  year={2008}
}
  • Published 2008
As a preliminary to the theory of stochastic integration, we recall the theory of Lebesgue-Stieltes integrals and its relation to bounded variation. Let G : [0,∞) → R be an increasing, right-continuous function. Recall that there is a unique measure μG on the Borel subsets of (0,∞) such that μG ((a, b]) = G(b) − G(a) whenever 0 < a < b. This measure μG is constructed in the same way as Lebesgue measure. The requirement, μG ((a, b]) = G(b) − G(a), defines a finitely additive measure on the… CONTINUE READING