TL;DR
This paper derives an explicit formula for the distribution of the time it takes for a Brownian motion to exceed its maximum value on a given interval, providing new insights into the process's extremal behavior.
Contribution
It introduces a novel explicit formula for the distribution of the first passage time after the maximum of a Brownian motion, advancing understanding of stochastic process extremities.
Findings
Explicit distribution formula for the time to exceed maximum
Enhanced understanding of Brownian motion extremal behavior
Potential applications in stochastic modeling and finance
Abstract
Let be the maximum value of an one-dimensional Brownian motion on the (time) interval . We derive an explicit formula for the distribution of the time required (after ) for the Brownian motion to exceed .
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Taxonomy
TopicsStochastic processes and financial applications · Random Matrices and Applications · Advanced Queuing Theory Analysis