Asymptotic approximation of degenerate fiber integrals

Asymptotic approximation of exponential integrals

1 Preliminaries 1 1.1 What this is . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Problem statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.3 Big-O and small-o notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.4 Definition: Asymptotic approximation ...

Asymptotic Approximation of Marginal Likelihood Integrals

We study the asymptotics of marginal likelihood integrals for discrete models using resolution of singularities from algebraic geometry, a method introduced recently by Sumio Watanabe. We briefly describe the statistical and mathematical foundations of this method, and explore how Newton diagrams and toric modifications help solve the problem. The approximations are then compared with exact com...

Hodge Integrals and Degenerate Contributions

Let X be a Calabi-Yau 3-fold containing a nonsingular genus g curve C ⊂ X. We study here the contribution of genus g + h covers of C to the genus g + h Gromov-Witten invariants of X. Degenerate contributions play an important role in the Gromov-Witten theory of Calabi-Yau 3-folds. In algebraic geometry, these contributions are related to Hodge integrals over the moduli space of curves Mg,n [FP]...

Asymptotic Expansions for Integrals

Degenerate kernel approximation method for solving Hammerstein system of Fredholm integral equations of the second kind

Degenerate kernel approximation method is generalized to solve Hammerstein system of Fredholm integral equations of the second kind. This method approximates the system of integral equations by constructing degenerate kernel approximations and then the problem is reduced to the solution of a system of algebraic equations. Convergence analysis is investigated and on some test problems, the propo...