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<p>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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月15日

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  • Stefan Ankirchner,
  • Julian Wendt

摘要

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.