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 ...

Clinical trials have traditionally followed a fixed design, in which patient allocation to treatments is fixed throughout the trial and specified in the protocol. The primary goal of this static ...

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

In this paper we evaluate the single-loss approximation method for high-quantile loss estimation on the basis of SAS OpRisk Global Data. Due to its simplicity, the single-loss approximation method has ...

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 their 2001 paper, Longstaff and Schwartz suggested a method for American option pricing using simulation and regression, and since then this method has rapidly gained importance. However, the idea ...

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 ...