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Националния семинар по стохастика

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Brownian Motion Conditioned to Spend Limited Time Outside a Bounded Interval – An Extreme Example of Entropic Repulsion

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Dominic Т. Schickentanz (TU Darmstadt).

Абстракт. We condition a Brownian motion on \(\mathbb{R}_{\ge 0}\) on spending a total of at most \(s>0\) time units outside a bounded interval. We describe the resulting process in terms of an SDE and discuss the surprising result in the context of entropic repulsion. Moreover, we explicitly determine the exact asymptotic behavior of the probability that a Brownian motion on \([0,T]\) spends limited time outside a bounded interval, as \(T\to \infty\).