7 problems

Conditional functional limit conjecture. The conditional distribution of

Functional normal-limit extension conjecture. The convergence

Weakening conjecture. The conditions of Theorem can be weakened to the mere divergence $n\alpha_n^2\to\infty$. This would extend the theorem's range of applicability, but the autho…

Jumping-in vanishing conjecture. The same assertions as Theorem hold.

Let $G$ be the state space, let $T_x$ denote the process associated with starting point $x\in G$, and let $\mathbf{n}$ be the excursion measure. For every sequence…

Let $(X_i)$ be a moving-average process with coefficients $(\varphi_j)_{j\in\mathbb Z}$, and let … varphij=0quadtext{for }j<0, … 0leqslant frac{sum{j=0}^{K}varphij}{sum{j=0}^{infty…

The A5 conjecture. If the tail condition holds with $\alpha=1$, then