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Time-varying fractionnally integrated processes with discrete and continuous argument| old_uid | 992 |
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| title | Time-varying fractionnally integrated processes with discrete and continuous argument |
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| start_date | 2006/03/31 |
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| schedule | 12h |
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| online | no |
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| location_info | 3e étage, salle 314 |
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| summary | Extending the works Philippe et al. (2005, 2006) on time-varying fractionally integrated operators $ A({\bf d}), B({\bf d}) $ with discrete argument depending on an arbitrary sequence ${\bf d} = (d_t, t \in {\Z}) $ of real numbers, we introduce nonhomogenous generalizations $I^{\alpha (·)} $ and $D^{\alpha (·)} $ of the Liouville fractional integral and derivative operators on the real line, where $\alpha (u), u\in {\R} $ a general function taking values in $(0,1)$ and satisfying some regularity conditions. The proof of $D^{\alpha (·)} I^{\alpha (·)}f = f$ relies on a surprising integral identity. We also discuss small and large scale limits of white noise integrals $X_t = \int_0^t (I^{\alpha (·)} \dot B)(s) {\d}s $ and $Y_t = \int_0^t (D^{\alpha (·)} \dot B)(s) {\d}s $. In the second part of the talk we extend the results of Philippe et al. (2005, 2006) on discrete time filtered processes $A({\bf d}) \veps_t$ and $B({\bf d}) \veps_t $ in two directions: (1) when ${\bf d} = (d_t, t \in {\Z}) $ is deterministic and
almost periodic at $+\infty $ and $-\infty$, and (2) when ${\bf d} = (d_t, t \in {\Z}) $ is random i.i.d.
Part of the results were obtained in collaboration with Anne Philippe, Marie-Claude Viano, Paul Doukhan, Gabriel Lang, Kristina Bruzaite and Marijus Vaiciulis. |
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| responsibles | Carlo, Bardet, Cottrell |
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