Events
DMS Analysis and Stochastic Analysis Seminar (SASA) |
| Time: Sep 17, 2025 (12:10 PM) |
| Location: 328 Parker Hall |
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Details:  Speaker: Davar Khoshnevisan (University of Utah)
Title: On the passage times of self-similar Gaussian processes on curved boundaries
Abstract: Let \(Tc,β\) denote the smallest \(t≥1\) that a continuous, self-similar Gaussian process with self-similarity index \(α>0\) moves at least \(±ctβ\) units. We prove that
(i) if \(β>α\), then \(Tc,β=∞\) with positive probability;
(ii) if \(β<α\), then \(Tc,β\) has moments of all order; and
(iii) if \(β=α\) and \(X\) is strongly locally nondeterministic in the sense of Pitt (1978), then there exists a continuous, strictly decreasing function \(λ:(0,∞)→(0,∞)\) such that \(E(Tc,βμ)\) is finite when \(0<μ<λ(c)\) and infinite when \(μ>λ(c)\).
Together these results extend a celebrated theorem of Breiman (1967) and Shepp (1967) for passage times of a Brownian motion on the critical square-root boundary. We briefly discuss two examples: one about fractional Brownian motion, and another about a family of linear stochastic partial differential equations.
More information about the talk can be found at:
Host: Le Chen
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