2 problems

Self-reinforced diffusion conjecture. If $\sum_{k=1}^{n}k^2a_k<0$, then $X_t$ converges almost surely; if $\sum_{k=1}^{n}k^2a_k>0$, then

Suppose that $f:\mathbb{R}\rightarrow\mathbb{R}$ is an odd function of compact support such that $xf(x)\ge 0$. Let $X$ be the process defined by the Durrett–Rogers equation. Durret…