Approximation theory and asymptotic methods form a foundational framework that bridges classical ideas with modern numerical analysis, enabling researchers to obtain practical, near‐optimal solutions ...

Stein's method has emerged as a powerful and versatile tool in probability theory for deriving error bounds in distributional approximations. Originally developed to ...

This course teaches commonly used approximation methods in quantum mechanics. They include time-independent perturbation theory, time-dependent perturbation theory, tight binding method, variational ...

An important part of the marginal maximum likelihood method described previously is the computation of the integral over the random effects. The default method in PROC NLMIXED for computing this ...

In this talk we present few instances of multilevel approximation methods involving PDEs with random parameters and associated scalar output quantities of interest (QoI). Multilevel methods aim at ...

It is of fundamental interest in statistics to test the significance of a set of covariates. For example, in genomewide association studies, a joint null hypothesis of no genetic effect is tested for ...

Covers asymptotic evaluation of integrals (stationary phase and steepest descent), perturbation methods (regular and singular methods, and inner and outer expansions), multiple scale methods, and ...

A critical issue in the credit risk industry is the accurate, efficient and robust pricing of collateralized debt obligations (CDOs) in a variety of mathematical models. These and many similar basket ...