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On fractional derivatives of the local time of a symmetric stable process as a doubly indexed process
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4. September 2012
Abstract.
In this paper, we prove two main results. The first one is to prove the regularity of fractional derivatives of local time of symmetric stable process with index 
; our result is similar to that of Marcus and Rosen (1992) for local time. The second result is to give a 
-variation of fractional derivatives of local time of symmetric stable process with index . Our approach is similar to that of Eisenbaum (2000) for local time.
Keywords: Local time; p-variation; symmetric stable process; fractional derivative; Hilbert transform
Received: 2011-11-11
Revised: 2012-06-15
Accepted: 2012-08-01
Published Online: 2012-09-04
Published in Print: 2012-09-01
© 2012 by Walter de Gruyter Berlin Boston
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- Masthead
- Large deviations for the backward stochastic differential equations
- Smooth approximations for fractional and multifractional fields
- The Kakutani–Hellinger affinity of processes of Itô processes driven by Poisson random measures
- The relaxed optimal control problem of forward-backward stochastic doubly systems with Poisson jumps and its application to LQ problem
- On fractional derivatives of the local time of a symmetric stable process as a doubly indexed process
Schlagwörter für diesen Artikel
Local time;
p-variation;
symmetric stable process;
fractional derivative;
Hilbert transform
Artikel in diesem Heft
- Masthead
- Large deviations for the backward stochastic differential equations
- Smooth approximations for fractional and multifractional fields
- The Kakutani–Hellinger affinity of processes of Itô processes driven by Poisson random measures
- The relaxed optimal control problem of forward-backward stochastic doubly systems with Poisson jumps and its application to LQ problem
- On fractional derivatives of the local time of a symmetric stable process as a doubly indexed process
