One-dimensional System Arising in Stochastic Gradient Descent

Konstantinos Karatapanis

We consider SDEs of the form $d{X}_t=|f(X_t)|/t^{\gamma }dt+1/t^{\gamma }d{B}_t$, where $f(x)$ behaves comparably to $|x{|}^k$ in a neighborhood of the origin, for $k\in [1,\infty )$. We show that th…