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I am looking for a concentration inequality of a double sum…. Let $X_1,\dots, X_n$ be iid r.v. and also let $Y_1,\dots ,Y_n$ be iid such that even $X_i$ and $Y_j$ are independent. I am looking for a ...

Let $d\mu$ be a Gaussian measure on $\mathbb{R}$ with the center $a \in \mathbb{R}$ and variance $1$. Let $B(a,r) \subset \mathbb{R}$ be the interval $[a-r,a+r]$. Then, for any smooth mapping $f : \...

Let $(X_t, t \ge 0)$ be a $\mathbb R^d$-valued stochastic process. Let $\lambda>0$. Assume we have $\mathbb E [|X_0|^2] < \infty$ and $$ \mathbb E [|X_t|^2] - \mathbb E [|X_0|^2] \le -2 \lambda \...

Given two SDEs $X^1$, $X^2$ : $$X^i_t=1+t+\int_0^t\sigma_i(s)dW_s,\quad \forall t\ge 0,$$ where $\sigma_i:\mathbb R_+\to [1/2,1]$ are non-decreasing s.t. $\sigma_1(t)\le \sigma_2(t)$ for all $t\ge 0$....

Let $\ell \geqslant 1$. Let us consider $(g_n)_{n \in \mathbb{N}}$ identically distributed independent real gaussian variables and real number $(a_{n_1,\dots n_{\ell}})_{(n_1, \dots, n_{\ell}s)\in\...