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  Volume 3, Issue 4, Article 62
On Some Inequalities of Local Times of Iterated Stochastic Integrals

    Authors: Litan Yan,  
    Keywords: Continuous local martingale, Continuous semimartingale, Iterated stochastic integrals, Local time, Random time, Burkholder-Davis-Gundy inequalities, Barlow-Yor inequalities.  
    Date Received: 06/07/01  
    Date Accepted: 25/06/02  
    Subject Codes:


    Editors: Neil S. Barnett,  

Let $ X=(X_t,{mathcal F}_t)_{tgeq 0}$ be a continuous local martingale with quadratic variation process $ langle X rangle$ and $ X_0=0$. Define iterated stochastic integrals $ I_n(X)=left(I_n(t,X),{mathcal F}_tright)$ $ (ngeq 0)$, inductively by

$displaystyle I_n(t,X)=int_0^tI_{n-1}(s,X)dX_s$
with $ I_0(t,X)=1$ and $ I_1(t,X)=X_t$. In this paper, we obtain some martingale inequalities for $ I_n(X)$, $ n=1,2,ldots$ and their local times at any random time.

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