A Sharp Upper Bound for the Expected Interval Occupation Time of Brownian Martingales

Stefan Ankirchner () and Julian Wendt ()
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Stefan Ankirchner: University of Jena
Julian Wendt: University of Jena

Journal of Theoretical Probability, 2025, vol. 38, issue 4, 1-36

Abstract: Abstract 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 of maximizing the expected occupation time in an interval.

Keywords: Occupation time in intervals; Diffusion control; Brownian martingales; Primary 60H05; Secondary 93E20 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10959-025-01446-5

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