Modern probabilistic models involve computation and analysis in very high-dimensional spaces. Here we explore several of ways in which analysis of problems high dimensional spaces can be made more tractable by various reductions. In particular, we focus on finite approximations for sampling point processes, particle methods for sampling high-dimensional distributions, situations in which hitting times for brownian motion in high dimensional space take on particularly simple forms, and certain maximal characteristics on the infinite-dimensional space of couplings of two random variables with fixed marginal distributions.
Loper, Jackson Hoy,
"Theory and Computation for Modern Probabilistic Models"
Applied Mathematics Theses and Dissertations.
Brown Digital Repository. Brown University Library.