STRASSEN'S FUNCTIONAL LIL FOR d-DIMENSIONAL SELF-SIMILAR GAUSSIAN PROCESS IN HOLDER NORM

Self-similar solutions‎ ‎of the Riemann problem for two-dimensional systems of conservation‎ ‎laws

In this paper, a new approach is applied to study the self-similar solutions of 2×2 systems of nonlinear hyperbolic conservation laws. A notion of characteristic directions is introduced and then used to construct local and smooth solutions of the associated Riemann problem

Point Process Models for Self - Similar 1

Self-similar processes based on fractal point processes (FPPs) provide natural and attractive network traac models. We show that the point process formulation yields a wide range of FPPs which in turn yield a diversity of parsimonious, computationally eecient, and highly practical asymptotic second-order self-similar processes. Using this framework, we show that the relevant second-order fracta...

High-Dimensional Gaussian Process Bandits

Many applications in machine learning require optimizing unknown functions defined over a high-dimensional space from noisy samples that are expensive to obtain. We address this notoriously hard challenge, under the assumptions that the function varies only along some low-dimensional subspace and is smooth (i.e., it has a low norm in a Reproducible Kernel Hilbert Space). In particular, we prese...

A Functional Lil for Symmetric Stable Processes

A functional law of the iterated logarithm is obtained for symmetric stable processes with stationary independent increments. This extends the classical liminf results of Chung for Brownian motion, and of Taylor for such remaining processes. It also extends an earlier result of Wichura on Brownian motion. Proofs depend on small ball probability estimates and yield the small ball probabilities o...

Gaussian Process Optimization for Self-Tuning Control