Abstract
In this article, we investigate some local time property and the regularity of the martingales satisfying the structure equation (see Emery [8]):
where \(\beta\) is a real parameter.
Moreover, using the Bouleau-Yor extension of Ito’s formula to a real function F satisfying: \( F(x)-F(y) = \int^x_y f (u)du\) with \(f\in L^{\infty}_{loc}(\mathfrak{R})\), we obtain inequalites of Burkholder-Davis-Gundy’s type for these martingales.
Mathematics Subject Classification (2000):
- 60GXX
- 60HXX
- 60JXX
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© 2001 Springer-Verlag Berlin/Heidelberg
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Chao, TM., Chou, CS. (2001). Some remarks on the martingales satisfying the structure equation \([X,X]_t = t + \int^t_0\beta X_{s^-} dX_s\). In: Azéma, J., Émery, M., Ledoux, M., Yor, M. (eds) Séminaire de Probabilités XXXV. Lecture Notes in Mathematics, vol 1755. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44671-2_4
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DOI: https://doi.org/10.1007/978-3-540-44671-2_4
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41659-3
Online ISBN: 978-3-540-44671-2
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