6 problems

Let $\mathbf{X}(t)$ be a deterministic function such that $\int_0^t ||\mathbf{X}(u)||^2du$ is strictly increasing and finite for $t\leq T<\infty$, and let $Z_{\mathbf{X}}(t)$ denot…

Let $f\in L^2_{\operatorname{imp}}$, let $(A_k)$ be pairwise disjoint Borel subsets of $\mathbb R_+$, and define $f_k=f\mathbf 1_{A_k}$. Let $(S_n)$ be the arrival times of a Poiss…

Let $N$ be a Poisson random measure and let $L^2_{\operatorname{imp}}$ be the space of bounded, square-integrable functions for which the relevant improper integrals exist. For a f…

General integrable unboundedness conjecture. A more general result on the potential integrable unboundedness of the set-valued convoluted stochastic integral with respect to the co…

Product square-integrability conjecture.

Let $f:\mathbb{R}rightarrow \mathbb{R}$ be twice continuously differentiable, with $|f'(x)|le K(1+|x|^{alpha})$ for some positive constants $K$ and $alpha$ and all $xinmathbb{R}$.…