Sample path properties of reflected Gaussian processes

Sample Path Large Deviations for Squares of Stationary Gaussian Processes

In this paper, we show large deviations for random step functions of type

Sample Path Properties of Anisotropic Gaussian Random Fields

The class of anisotropic Gaussian random fields includes fractional Brownian sheets, certain operator-self-similar Gaussian random fields with stationary increments and the random string process. They arise naturally in many areas and can serve as more realistic models than fractional Brownian motion. We will discuss sample path properties of an (N, d)-fractional Brownian sheet BH = {BH(t), t ∈...

Local times and Sample Function Properties of Stationary Gaussian Processes

Sample Path and Fractal Properties of Lévy Processes

The sample paths of Lévy processes generate various random fractals and many of their properties have been studied since 1960’s [see the survey papers of Fristedt (1974), Taylor (1986) and Xiao (2004)]. The lectures will cover the following topics: Hausdorff dimension and exact Hausdorff measure functions for random fractals determined by Lévy processes; Hausdorff dimension computation using po...

Sample Efficient Reinforcement Learning with Gaussian Processes

This paper derives sample complexity results for using Gaussian Processes (GPs) in both modelbased and model-free reinforcement learning (RL). We show that GPs are KWIK learnable, proving for the first time that a model-based RL approach using GPs, GP-Rmax, is sample efficient (PAC-MDP). However, we then show that previous approaches to model-free RL using GPs take an exponential number of step...