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 ...

Kesten proposed a method for adjusting the coefficients of a scalar stochastic approximation process, and proved w.p. 1 convergence. A family of multidimensional processes for function minimization ...

Linear mixed models have attracted considerable attention recently as a powerful and effective tool for accounting for population stratification and relatedness in genetic association tests. However, ...

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 ...

The stochastic root-finding problem is that of finding a zero of a vector-valued function known only through a stochastic simulation. The simulation-optimization problem is that of locating a ...

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 topic we will advance the fundamental mathematical understanding of artificial neural networks, e.g., through the design and rigorous analysis of stochastic gradient descent methods for their ...

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 ...