We propose an adaptive Monte Carlo algorithm for estimating multidimensional integrals over a hyper-rectangular region. The lgorithm uses iteratively the idea of separating the domain of integration into 2subregions. The proposed algorithm can be applied irectly to estimate the integral using an efficient way of storage. We test the algorithm for estimating the value of a 30-dimensional ntegral...

For Halloween, we come as a math course 1 Monte Carlo Integration Suppose we want to evaluate a definite integral,

The purpose of this article is to present a new Fast Fourier Transform approach to finding option prices with respect to a given objective density of the underlying asset, and a Stochastic Discount Factor. This is compared to a Monte Carlo approach and shown to be a more general approach which can often evaluate prices more quickly in many cases. However it does come with some computational iss...

We propose algorithms of adaptive integration for calculation of the tail probability in multi-factor credit portfolio loss models. We first devise the classical Genz-Malik rule, a deterministic multiple integration rule suitable for portfolio credit models with number of factors less than 8. Later on we arrive at the adaptive Monte Carlo integration, which simply replaces the deterministic int...

background: palladium-103 (103pd) is a brachytherapy source for cancer treatment. the monte carlo codes are usually applied for dose distribution and effect of shieldings. monte carlo calculation of dose distribution in water phantom due to a med3633 103pd source is presented in this work. materials and methods: the dose distribution around the 103pd model med3633 located in the center of 30×30...

where σ denotes the normalized surface measure on Sd and f is a continuous real valued function. As a general reference on Quasi-Monte Carlo methods we mention Niederreiter [22]. The problem of distributing points on the sphere is also related to constructive multivariate approximation, see Reimer [24]. For the recent literature on spherical problems concerned with approximation and numerical i...

Monte Carlo integration has been a common approach for light transport simulation over many years. This widespread usage, however, seems to come with certain misconceptions regarding the behavior of error in Monte Carlo algorithms. In particular, unbiased Monte Carlo integration has been blindly (and often implicitly) considered as a holy grail of accurate light transport simulation by some peo...

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The standard Kernel Quadrature method for numerical integration with random point sets (also called Bayesian Monte Carlo) is known to converge in root mean square error at a rate determined by the ratio s/d, where s and d encode the smoothness and dimension of the integrand. However, an empirical investigation reveals that the rate constant C is highly sensitive to the distribution of the rando...