Nonlocal ergodic control problem in ${\mathbb{R}}^d$

Anup Biswas, Erwin Topp

We study the existence-uniqueness of solution $(u,\lambda )$ to the ergodic Hamilton-Jacobi equation $$(-\Delta {)}^{s}u+H(x,\nabla u)=f-\lambda \text{in}{\mathbb{R}}^d,$$ and $u\ge 0$, whe…