Small Deviations of Sums of Correlated Stationary Gaussian Sequences

DOI10.1137/S0040585X97T988356zbMath1377.60048arXiv1606.01072MaRDI QIDQ4602296

Frank Aurzada, Mikhail Lifshits

Publication date: 9 January 2018

Published in: Theory of Probability & Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.01072

zbMATH Keywords

fractional Brownian motionGaussian processfractional Gaussian noisestationary Gaussian sequencesmall deviation probability

Mathematics Subject Classification ID

Gaussian processes (60G15) Central limit and other weak theorems (60F05) Fractional processes, including fractional Brownian motion (60G22) Stationary stochastic processes (60G10) Sums of independent random variables; random walks (60G50)

Related Items (max. 100)

Quenched Small Deviation for the Trajectory of a Random Walk with Random Environment in Time ⋮ On the history of St. Petersburg school of probability and mathematical statistics. II: Random processes and dependent variables

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Time series: theory and methods.
• Convex measures on locally convex spaces
• New Gaussian estimates for enlarged balls
• Small deviation probability via chaining
• On probabilities of small deviations for stochastic processes
• Stochastic-Process Limits
• On the Maximum Partial Sums of Sequences of Independent Random Variables
• Weak convergence to fractional brownian motion and to the rosenblatt process
• Small Deviations in a Space of Trajectories
• Existence of small ball constants for fractional Brownian motions
• A simple proof of the Gaussian correlation conjecture extended to multivariate gamma distributions
• Royen’s Proof of the Gaussian Correlation Inequality
• Long Range Dependence
• On the Maximum Partial Sums of Sequences of Independent Random Variables
• Regularly varying functions

This page was built for publication: Small Deviations of Sums of Correlated Stationary Gaussian Sequences