Self-similar martingales derived from Root embedding

Antoine-Marie Bogso, Mbehou Mohamed

Given a family $({\mu }_{\lambda },\lambda \ge 0)$ of integrable mean-zero probability measures such that, for every $\lambda \ge 0$, ${\mu }_{\lambda }$ is the image of ${\mu }_1$ under the homothety $y⟼\sqrt{\lambda }y$, we…