A sharp upper bound for the expected interval occupation time of Brownian martingales

Stefan Ankirchner (1) , Julian Wendt (1)

1 Friedrich-Schiller-Universität = Friedrich Schiller University Jena [Jena, Germany]

We consider Brownian integral processes with integrands that are bounded and bounded away from zero. We provide an upper estimate for the expected occupation time in an interval. The estimate does not depend on the integrand but only on its bounds. We derive the estimate by solving a stochastic control problem that consists in maximizing the expected occupation time in an interval.

Domaines: Probabilités [math.PR]

Stefan Ankirchner, Julian Wendt. A sharp upper bound for the expected interval occupation time of Brownian martingales. 2021. ⟨hal-03138433⟩