Stochastic Integrals

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


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.



Simple Process Finite Interval Quadratic Variation Continuous Version Stochastic Integral 
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  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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