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Bounds for boundary non-crossing probabilities of general Gaussian process and large deviation asymptotics

Georgiy Shevchenko (National University of Kiev)
Thursday 25 April 2019 13:15–14:00 Aud. D3 (1531-215)
Stochastics Seminar
The talk is based on joint result with Yuliya Mishura (Kiev University) and Enkelejd Hashorva (Lausanne University). We study probabilities $P(\forall t \in \mathbb{T}, X_f + f(t) \le u(t))$ of non-crossing a boundary $u$ by a centered Gaussian process $X$, indexed by a separable metric space $\mathbb{T}$, with drift $f$. We establish upper and lower bounds for non-crossing probabilities, which are matching in the sense that they determine precise logarithmic asymptotics for probabilities in the case of large drift.

Contact: Mark Podolskij Revised: 24.06.2021