Probability Commons^™

Stochastic Functional Differential Equations On Manifolds, Rémi Léandre, Salah-Eldin A. Mohammed

Articles and Preprints

In this paper, we study stochastic functional differential equations (sfde's) whose solutions are constrained to live on a smooth compact Riemannian manifold. We prove the existence and uniqueness of solutions to such sfde's. We consider examples of geometrical sfde's and establish the smooth dependence of the solution on finite-dimensional parameters.

Empirical Spectral Analysis Of Random Number Generators, David Zeitler

Dissertations

Computer simulation procedures have become a staple of research and development in many fields, including statistics. The generation of pseudo random number sequences is the core of computer simulation procedures. Validity of research results often depend on the underlying validity of the generator being used.

In this work we develop the machinery for a class of tests of spatial uniformity based on a multi-dimensional Fourier transform of the empirical probability density function. The test can be adapted to specific requirements and has the added advantage that it has computational complexity that is relatively independent of the number of data points …

Discrepancy Convergence For The Drunkard's Walk On The Sphere, Francis E. Su

All HMC Faculty Publications and Research

We analyze the drunkard's walk on the unit sphere with step size θ and show that the walk converges in order C/sin²(θ) steps in the discrepancy metric (C a constant). This is an application of techniques we develop for bounding the discrepancy of random walks on Gelfand pairs generated by bi-invariant measures. In such cases, Fourier analysis on the acting group admits tractable computations involving spherical functions. We advocate the use of discrepancy as a metric on probabilities for state spaces with isometric group actions.

A Coin Flipping Game With Non Transitive Odds, Stacy Jurgens

Honors Capstones

Capstone submitted as a graduation requirement for the BSU Honors Program.