David Janz

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20232026

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math.PR2026

Self-normalised Bennett inequalities for Hilbert-valued martingales

David Janz

We prove time-uniform self-normalised Bennett inequalities for a martingale $(M_{n})_{n \geq 0}$ in a separable Hilbert space, with $M_{0} = 0$ and increments bounded in norm by one. Writi…

math.PR2025

Bernstein-type dimension-free concentration for self-normalised martingales

Arya Akhavan, Amitis Shidani, Alex Ayoub +1

We introduce a dimension-free Bernstein-type tail inequality for self-normalised martingales, where the normalisation uses the predictable quadratic variation and the radius depend…