6 problems

Self-avoiding walk variation conjecture. We conjecture that

Let $Y$ be the Wiener–Weierstrass bridge in the critical case $H=K$, and set $p=1/H$. Its critical $p$-variation is infinite. Schied–Zhang's logarithmic correction conjecture. The…

Let $Y$ be the Wiener–Weierstrass bridge with $H=K$, let $b\geq 2$, and consider its $b$-adic $(1/H)$-variation. For $t\in[0,1]$, the normalized sums use a sequence $a_n$. Schied–Z…

Let $Y$ be the Wiener–Weierstrass bridge, with parameters $H$ and $K$, and suppose $H>K$. Its limiting $b$-adic $(1/K)$-variation is $Vt$, where $V$ is a finite positive random var…

Let $1\le p<\infty$, and let $\Lambda_p BV[0,1]$ be the Banach algebra of all functions of bounded variation in the Shiba–Waterman sense. Open multiplication conjecture. The multip…

Let $\varphi:[0,+\infty)\to[0,+\infty)$ be a Young function, meaning a convex, strictly increasing function with $\varphi(0)=0$. For a function $f$, define its $\varphi$-variation…