11 problems

Bouleau–Hirsch energy image density conjecture. Every Dirichlet structure satisfies the energy image density property.

Let $d=1$, let $(\mathcal{F}_t)_{t\in\mathcal{T}}$ be the filtration generated by $W$, and let $\bm{x},h\in\mathcal{X}$ and $\phi\in\mathcal{C}^1_{b,\mathcal{X}}(\mathcal{X})$. Sup…

Bouleau–Hirsch energy image density conjecture. The invertibility of the generalized Malliavin matrix of $f$ should imply that the law of $f$ is absolutely continuous with respect…

Let $X$ solve the quasilinear Skorohod SDE … where $X_0\in L^p(\Omega)$ for some $p>2$, $a$ satisfies the global Lipschitz and boundedness condition … for all $t\in[0,1]$,…

Let $F_\infty$ be the target random variable in the second Wiener chaos of the form referenced in the source, and let $F=I_q(f)$ be a chaotic random variable in the $q$th Wiener ch…

Stein universality lemma. For every $h\in\mathcal{H}$, this equation admits a bounded solution $f_h$ that is $d$ times differentiable, with

Let $b$ be a drift coefficient lying in $L_p^q$. For $i=1,ldots,d$, define … and set … Here $Y^b$ is the expectation appearing on the right-hand side of the paper's equation defini…

Fix $q\geq 2$. Let $\{F_n\}_{n\geq 1}$ be a sequence with $F_n=I_q(f_n)$, where $f_n\in \mathcal{H}^{\odot q}$, and suppose that … Let $Y$ have the symmetric Gamma distribution…

A smooth Brownian martingale is a martingale admitting the smooth representation developed in the paper, and the backward Taylor expansion (BTE) is the discrete-time expansion used…

Let $X$ be a continuous Gaussian process with stationary increments, and let $Q(t)=\operatorname{Var}(X_t)$. Assume the hypotheses and notation preceding the conjecture, including…

Asymptotic-strictness conjecture. This inequality should be asymptotically strict as $t$ tends to infinity: