This dissertation introduces a theoretical framework to study different sampling patterns in the spherical domain and their effects in the evaluation of global illumination integrals. Evaluating illumination (light transport) is one of the most essential aspect in image synthesis to achieve realism which involves solving multi-dimensional space integrals. Monte Carlo based numerical integration...

To reduce randomness drastically in Monte Carlo (MC) integration, we propose a pairwise independent sampling, the dynamic random Weyl sampling (DRWS). DRWS is applicable even if the length of random bits to generate a sample may vary. The algorithm of DRWS is so simple that it works very fast, even though the pseudo-random generator, the source of randomness, might be slow. In particular, we ca...

The analysis of general dynamic models involves a sequence of posterior distributions corresponding to the subsequent stages of the dynamic model. In the absence of normal/linear structure numerical integration schemes are required to estimate features of these posterior distributions. This paper reviews some previously suggested Monte Carlo based algorithms and suggests a new scheme which make...

New regulations, stronger competitions and more volatile capital markets have increased the demand for stochastic asset-liability management (ALM) models for insurance companies in recent years. The numerical simulation of such models is usually performed by Monte Carlo methods which suffer from a slow and erratic convergence, though. As alternatives to Monte Carlo simulation, we propose and in...

The Brownian bridge has been suggested as an effective method for reducing the quasi-Monte Carlo error for problems in finance. We give an example of a digital option where the Brownian bridge performs worse than the standard discretization. Hence, the Brownian bridge does not offer a consistent advantage in quasi-Monte Carlo integration. We consider integrals of functions of d variables with G...

background: the monte carlo method is the most accurate method for simulation of radiation therapy equipment. the linear accelerators are currently the most widely used machines in radiation therapy centers. methods: in this work, a monte carlo modelling of the siemens oncor linear accelerator in 6 mv and 18 mv beams was performed. the results of simulation were validated by measurements in wat...

Quasi-Monte Carlo rules which can achieve arbitrarily high order of convergence have been introduced recently. The construction is based on digital nets and the analysis of the integration error uses Walsh functions. Various approaches have been used to show arbitrarily high convergence. In this paper we explain the ideas behind higher order quasi-Monte Carlo rules by leaving out most of the te...

A Monte Carlo program is presented that computes all four fermion processes in e + e − annihilation. QED initial state corrections and QCD contributions are included. Fermions are taken to be massless, allowing a very fast evaluation of the matrix element. A systematic, modular and self-optimizing strategy has been adopted for the Monte Carlo integration, that serves also as an example for furt...

This study is an analysis of the natural difficulties of integration by Monte Carlo or quasi-Monte Carlo methods. In spite of what is sometimes written, these methods work only in some precise cases. For the important problem of the computation of expectations of functionals of stochastic processes, we present the advantages of a method based on the implementation of the Bernoulli shift operato...

We examine current paradigms in parallel strategies for multivariate integration algorithms. These include various process structures (centralized vs. global) and work distribution strategies (static or dynamic) in synchronous or asynchronous implementations. The target algorithm classes are Monte Carlo, quasi-Monte Carlo and adaptive. Strengths and weaknesses of the resulting parallel algorith...