[2608.15874] Self-normalised Bennett inequalities for Hilbert-valued martingales

View PDFHTML (experimental)Abstract:We prove time-uniform self-normalised Bennett inequalities for a martingale $(M_n)_{n\geq0}$ in a separable Hilbert space, with $M_0=0$ and increments bounded in norm by one. Writing $V_n$ for its predictable covariance process and $h(u)=(1+u)\log(1+u)-u$ for the Bennett rate function, we show that, fo...

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