A sharp bound on the expected local time of a continuous ${\mathcal{L}}_2$-bounded Martingale

David Gilat, Isaac Meilijson, Laura Sacerdote

For a continuous ${\mathcal{L}}_2$-bounded Martingale with no intervals of constancy, starting at $0$ and having final variance ${\sigma }^2$, the expected local time at $x\in \mathcal{R}$ is at m…