Quantum scattering at zero energy is studied with stochastic methods. A path integral representation for the scattering cross section is developed. It is demonstrated that Monte Carlo simulation can be used to compare effective potentials which are frequently used in multiple scattering with the exact result.

In this paper we study the problem of minimizing the average of a large number (n) of smooth convex loss functions. We propose a new method, S2GD (Semi-Stochastic Gradient Descent), which runs for one or several epochs in each of which a single full gradient and a random number of stochastic gradients is computed, following a geometric law. The total work needed for the method to output an ε-ac...

In this paper, we propose to enhance particle-based stochastic optimization methods (SO) by using Principal Component Analysis (PCA) to build an approximation of the cost function in a neighborhood of particles during optimization. Then we use it to shift the samples in the direction of maximum cost change. We provide theoretical basis and experimental results showing that such enhancement impr...

Stochastic programming is concerned with practical procedures for decision-making under uncertainty , by modelling uncertainties and risks associated with decisions in a form suitable for optimization. The eld is developing rapidly with contributions from many disciplines such as operations research, probability and statistics, and economics. A stochastic linear program with recourse can equiva...

The method of conjugate gradients provides a very effective way to optimize large, deterministic systems by gradient descent. In its standard form, however, it is not amenable to stochastic approximation of the gradient. Here we explore a number of ways to adopt ideas from conjugate gradient in the stochastic setting, using fast Hessian-vector products to obtain curvature information cheaply. I...

Anum ber of spectral modeling approaches in the engineering and estimation lit.erature are potentially applicable to stochas. ic synthesis in computer graphics. Two specific approaches are developed. The orthogonality principle of estimation theory is used to derive a stochastic subdivision construction with specified autocorrelation and spectrum properties; this approach also provides an alter...

Estimation of the volatility of time series has taken off since the introduction of the GARCH and stochastic volatility models. While variants of the GARCH model are applied in scores of articles, use of the stochastic volatility model is less widespread. In this article it is argued that one reason for this difference is the relative difficulty of estimating the unobserved stochastic volatilit...