Krzysztof Burdzy, Davar Khoshnevisan
Abstract
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Let D be the Wiener sausage of width $\varepsilon$ around two-sided Brownian motion. The components of two-dimensional reflected Brownian motion in D converge to one-dimensional Brownian motion and iterated Brownian motion, respectively, as $\varepsilon$ goes to 0.
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Let D be the Wiener sausage of width $\varepsilon$ around two-sided Brownian motion. The components of two-dimensional reflected Brownian motion in D converge to one-dimensional Brownian motion and iterated Brownian motion, respectively, as $\varepsilon$ goes to 0.
Key concepts: Mathematics, Reflected Brownian motion, Brownian motion, Brownian excursion, Iterated function, Diffusion process, Martingale representation theorem, Fractional Brownian motion