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- W54547934 abstract "We prove the almost sure invariance principle for martingales with stationary ergodic differences taking values in a separable 2-smooth Banach space (for instance a Hilbert space). A compact law of the iterated logarithm is established in the case of stationary differences of reverse martingales. Then, we deduce the almost sure invariance principle for stationary processes under, the Hannan condition, and a compact law of the iterated logarithm for stationary processes arising from non-invertible dynamical systems. Those results for stationary processes are new, even in the real valued case. We also obtain the Marcinkiewicz-Zygmund strong law of large numbers for stationary processes with values in some smooth Banach spaces." @default.
- W54547934 created "2016-06-24" @default.
- W54547934 creator A5082726825 @default.
- W54547934 date "2012-09-17" @default.
- W54547934 modified "2023-09-27" @default.
- W54547934 title "ASIP for martingales in 2-smooth Banach spaces. Applications to stationary processes" @default.
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