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1 results

  • 5 - Consistency of Multivariate Special Semimartingales

  • from Part One - Consistencies
  • Tomasz R. Bielecki, Illinois Institute of Technology, Jacek Jakubowski, Uniwersytet Warszawski, Poland, Mariusz Niewȩgłowski
  • Book:
    Structured Dependence between Stochastic Processes
    Published online:
    18 September 2020
    Print publication:
    27 August 2020, pp 67-76

  • Summary

    In this chapter we introduce and discuss various concepts of consistency for multivariate special semimartingales. The results here are mainly based on Theorem 5.1, which generalizes to the case of semimartingales that are not special. Thus, these results themselves generalize in a straightforward manner to the case of semimartingales that are not special. We chose to work with special semimartingales in order to ease somewhat the presentation. Throughout this chapter the semimartingale truncation functions will be considered to be standard truncation functions of appropriate dimensions. In what follows, the semimartingale characteristics will be always computed with respect to the relevant standard truncation functions. Thus, the semimartingale characteristics for all the semimartingales showing in the rest of this chapter are considered to be unique (as functions of the trajectories on the canonical space) once the filtration is chosen with respect to which the characteristics are computed. The theory is illustrated by various examples.