The Monte Carlo method has long been recognised as a powerful technique for performing certain calculations, generally those too complicated for a more classical approach. Since the use of high-speed computers became widespread in the 1950s, a great deal of theoretical investigation has been undertaken and practical experience has been gained in the Monte Carlo approach. The aim of this review ...

Quantum Monte Carlo is an important and complementary alternative to density functional theory when performing computational electronic structure calculations in which high accuracy is required. The method has many attractive features for probing the electronic structure of real atoms, molecules and solids. In particular, it is a genuine many-body theory with a natural and explicit description ...

We discuss a sampling algorithm which generates flat histogram in energy. In combination with transition matrix Monte Carlo, the density of states and derived quantities such as entropy and free energy as a function of temperature can be computed in a single simulation.

Quasi-Monte Carlo is usually employed to speed up the convergence of Monte Carlo in approximating multivariate integrals. While convergence of the Monte Carlo method is O(N−1/2), that of plain quasi-Monte Carlo can achieve O(N−1). Several methods exist to increase its convergence to O(N−α ), α > 1, if the integrand has enough smoothness. We discuss two methods: lattice rules with periodization ...

In this paper, we apply a combined Monte Carlo and Quasi-Monte Carlo method, which we proposed in an earlier paper [32], to the evaluation of an European Call option and of an Asian Call option. We assume that the stock price of the underlying asset S = S(t) is driven by a Lévy process Z(t), with independent increments distributed according to a NIG distribution. We compare our method with the ...

In this paper, we apply a combined Monte Carlo and Quasi-Monte Carlo method, developed by us in a previous paper [31], to the evaluation of barrier options. We assume that the stock price of the underlying asset is driven by a Lévy process with independent increments distributed according to a NIG distribution. We also provide numerical results that compare our method with the Monte Carlo metho...

We present a formalism of the transition matrix Monte Carlo method. A stochastic matrix in the space of energy can be estimated from Monte Carlo simulation. This matrix is used to compute the density of states, as well as to construct multi-canonical and equal-hit algorithms. We discuss the performance of the methods. The results are compared with single histogram method, multi-canonical method...

in the present work‎, ‎a new stochastic algorithm is proposed to solve multiple dimensional fredholm integral equations of the second kind‎. ‎the solution of the‎ integral equation is described by the neumann series expansion‎. ‎each term of this expansion can be considered as an expectation which is approximated by a continuous markov chain monte carlo method‎. ‎an algorithm is proposed to sim...