High minima of non-smooth Gaussian processes

@article{Wu2019HighMO,
  title={High minima of non-smooth Gaussian processes},
  author={Zhixin Wu and Arijit Chakrabarty and Gennady Samorodnitsky},
  journal={Electronic Communications in Probability},
  year={2019}
}
In this short note we study the asymptotic behaviour of the minima over compact intervals of Gaussian processes, whose paths are not necessarily smooth. We show that, beyond the logarithmic large deviation Gaussian estimates, this problem is closely related to the classical small-ball problem. Under certain conditions we estimate the term describing the correction to the large deviation behaviour. In addition, the asymptotic distribution of the location of the minimum, conditionally on the… Expand
Large Deviations for High Minima of Gaussian Processes with Nonnegatively Correlated Increments
In this article we prove large deviations principles for high minima of Gaussian processes with nonnegatively correlated increments on arbitrary intervals. Furthermore, we prove large deviationsExpand

References

SHOWING 1-10 OF 10 REFERENCES
Asymptotic behaviour of high Gaussian minima
We investigate what happens when an entire sample path of a smooth Gaussian process on a compact interval lies above a high level. Specifically, we determine the precise asymptotic probability ofExpand
Gaussian processes: Inequalities, small ball probabilities and applications
Publisher Summary This chapter focuses on the inequalities, small ball probabilities, and application of Gaussian processes. It is well-known that the large deviation result plays a fundamental roleExpand
Tail behavior of sums and differences of log-normal random variables
We present sharp tail asymptotics for the density and the distribution function of linear combinations of correlated log-normal random variables, that is, exponentials of components of a correlatedExpand
Reproducing kernel Hilbert spaces of Gaussian priors
We review definitions and properties of reproducing kernel Hilbert spaces attached to Gaussian variables and processes, with a view to applications in nonparametric Bayesian statistics using GaussianExpand
Regular Variation in R k
Researchers investigating certain limit theorems in probability have discovered a multivariable analogue to Karamata's theory of regularly varying functions. The method uses elements of real analysisExpand
ON THE EXISTENCE OF PATHS BETWEEN POINTS IN HIGH LEVEL EXCURSION SETS OF GAUSSIAN RANDOM FIELDS
Research supported in part by US-Israel Binational Science Foundation, 2008262, by ARO grant W911NF-07-1-0078, NSF grant DMS-1005903 and NSA grant H98230-11-1-0154 at Cornell University, by IsraelExpand
Small ball probabilities for Gaussian Markov processes under the Lp-norm
Let {X(t); 0[less-than-or-equals, slant]t[less-than-or-equals, slant]1} be a real-valued continuous Gaussian Markov process with mean zero and covariance [sigma](s,t)=EX(s)X(t)[not equal to]0 for 0Expand
Characteristic Functions
  • M. Huzak
  • Computer Science
  • International Encyclopedia of Statistical Science
  • 2011
Reproducing kernel Hilbert spaces of Gaussian priors. In Pushing the Limits of Contemporary Statistics: Contributions in Honor of Jayanta K. Ghosh, volume 3 of IMS Collections
  • 1970
The Expected Number of Zeros of a Stationary Gaussian Process