On the combinatorics of iterated stochastic integrals

F. Jamshidian

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    3 Citations (Scopus)
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    Abstract

    This paper derives several identities for the iterated integrals of a general semimartingale. They involve powers, brackets, exponential and the stochastic exponential. Their form and derivations are combinatorial. The formulae simplify for continuous or finite-variation semimartingales, especially for counting processes. The results are motivated by chaotic representation of martingales, and a simple such application is given.
    Original languageEnglish
    Pages (from-to)1-15
    Number of pages15
    JournalStochastics
    Volume83
    Issue number1
    DOIs
    Publication statusPublished - 2011

    Keywords

    • Itô's formula
    • EWI-22233
    • stochastic exponential
    • MSC-60H05
    • Semimartingale
    • IR-81467
    • chaotic representation
    • iterated integrals
    • METIS-289684
    • power jump processes
    • MSC-60C05

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