Stochastic Integrals

  • Gopinath Kallianpur
Part of the Stochastic Modelling and Applied Probability book series (SMAP, volume 13)

Abstract

Let L denote the family of all real-valued functions Y t (ω) defined on R + × Ω which are measurable with respect to ℬ(R +) × A and have the following properties:
  1. 1.

    Y = (Y t ) is adapted to (G t ).

     
  2. 2.

    For each ω,the function tY t (ω) is left-continuous.

     

Keywords

Simple Process Finite Interval Quadratic Variation Continuous Version Stochastic Integral 
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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Notes

  1. Section 3.1 is based on the ideas of Dellacherie [7] and Courrège [5]. The proofs of the theorems stated in 3.1 are to be found in [7]. The process ((4) of Theorem 3.1.4 is called the dual predictable projection of (Ut) by Dellacherie [7]. Section 3.2 is based on Meyer [43, 44] and Courrège [5]. A full discussion of Ito’s stochastic integral is given in Ito [20]. Lemma 3.3.1 is from Gihman and Skorohod [15]. Lemma 3.3.3 is given in Friedman [13].Google Scholar

Copyright information

© Springer Science+Business Media New York 1980

Authors and Affiliations

  • Gopinath Kallianpur
    • 1
  1. 1.Department of StatisticsUniversity of North CarolinaChapel HillUSA

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