Abstract
We prove the following result: For $(Z_{t})_{t\in\mathbf{R}}$ a fractional Brownian motion with arbitrary Hurst parameter, for any stopping time $\tau$, there exist arbitrarily small $\varepsilon>0$ such that $Z_{\tau+\varepsilon}<Z_{\tau}$, with asymptotic behaviour when $\varepsilon\searrow0$ satisfying a bound of iterated logarithm type. As a consequence, fractional Brownian motion satisfies the “two-way crossing” property, which has important applications in financial mathematics.
Citation
Rémi Peyre. "Fractional Brownian motion satisfies two-way crossing." Bernoulli 23 (4B) 3571 - 3597, November 2017. https://doi.org/10.3150/16-BEJ858
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