I am reading a paper on stochastic optimization. And in this paper, the proofs are based on the Pinelis' 1994 inequality. I read the paper by Pinelis for more information and it is with great frustration that I was not able to find the inequality corresponding to that mentioned in the paper I am reading.

Here's the inequality in the article I'm reading:

$$ \begin{array}l \text{(The Pinelis' 1994 inequality). Let } X_1,\dots, X_T \in \mathbb{R}^d \\ \text{be a random process satisfying } \mathbb{E}[X_t\mid X_1,\dots,X_{t−1} ] = 0 \text{ and} \\ \|X_t\| ≤ M. \text{ Then } \mathbb{P}[\| X_1 + \cdots + X_T\|^2 > 2 \log(2 /\delta)M^2T] \leq \delta. \end{array} $$

Nowhere in Pinelis' 1994 paper is this inequality mentioned.

So I ask myself, does this inequality really exist? Do you know it?