Bounds on the suprema of Gaussian processes, and omega results for the sum of a random multiplicative function
By Adam J Harper. 2010
55 citations recorded by the source corpus.
We prove new lower bounds for the upper tail probabilities of suprema of Gaussian processes. Unlike many existing bounds, our results are not asymptotic, but supply strong information when one is only a little into the upper tail. We present an extended application to a Gaussian version of a random process studied by Halasz. This leads to much improved lower bound results for the sum of a random multiplicative function. We further illustrate our methods by improving lower bounds for some classical constants from extreme value theory, the Pickands constants $H_{\alpha}$, as $\alpha\rightarrow 0$.
Subfields: Finance, Management Science and Operations Research
View Paper: https://www.semanticscholar.org/paper/e715579a92f6e2e642608e68d0104646fea5dc8e
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In Finance
In Management Science and Operations Research
Citations in the corpus
- MOMENTS OF RANDOM MULTIPLICATIVE FUNCTIONS, I: LOW MOMENTS, BETTER THAN SQUAREROOT CANCELLATION, AND CRITICAL MULTIPLICATIVE CHAOS (2017, methodology): “ng form of the Prime Number Theorem implies that both X x1/e j <p≤xj cos((t+ tj)logp) p1+2σ , X x1/e j <p≤xj cos(2tj logp) p1+2σ ≪ 1 |t|logxj ≪ 1 ej|t|logx 1 ≪ 1 Cej . See section 6.1 of Harper [10] for details of such calculations. Having made these preliminary observations, we can check the ”
- Generalized Pickands constants and stationary max-stable processes (2016, background): “tion of Pickands constants, with particular focus on the case δ = 0; see for instance Shao (1996); Hu¨sler and Piterbarg (1999); D¸ebicki et al. (2003); D¸ebicki (2005); D¸ebicki and Kisowski (2008); Harper (2013, 2015). Recently, the seminal contribution Dieker and Yakir (2014) derived the alternat”