Abstract
We propose new concentration inequalities for self-normalized martingales. The main idea is to introduce a suitable weighted sum of the predictable quadratic variation and the total quadratic variation of the martingale. It offers much more flexibility and allows us to improve previous concentration inequalities. Statistical applications on autoregressive process, internal diffusion-limited aggregation process, and online statistical learning are also provided.
Highlights
Let (Mn) be a locally square integrable real martingale adapted to a filtration F = (Fn) with M0 = 0
We propose new concentration inequalities for self-normalized martingales
Since the pioneer work of Azuma and Hoeffding [1], [16], a wide literature is available on concentration inequalities for martingales
Summary
We will show that inequality (1.3) is a special case of a more general result involving a suitable weighted sum of [M ]n and n. It was shown by De la Peña and Pang [11] that for any positive x, P.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
