A simulation based method for the numerical solution of PDE with random coefficients is presented. By the Feynman-Kac formula, the solution can be represented as conditional expectation of a functional of a corresponding stochastic differential equation driven by independent noise. A time discretization of the SDE for a set of points in the domain and a subsequent Monte Carlo regression lead to...

Quantum computing is a promising way to systematically solve the longstanding computational problem, ground state of many-body fermion system. Many efforts have been made realise certain forms quantum advantage in this for instance, development variational algorithms. A recent work by Huggins et al. [1] reports novel candidate, i.e. quantum-classical hybrid Monte Carlo algorithm with reduced bi...

The uniform random number can be manipulated to simulate the characteristics of any probability density function. For power system reliability analysis the exponential and the Weibull distributions are well suited. Simulated exponential and Weibull random variables can be obtained from uniform (0,1) RNs by making use of the fact that the cumulative density function (CDF) is uniform between zero...

In recent years, parallel processing has become widely available to researchers. It can be applied in an obvious way in the context of Monte Carlo simulation, but techniques for “parallelizing” Markov chain Monte Carlo (MCMC) algorithms are not so obvious, apart from the natural approach of generating multiple chains in parallel. While generation of parallel chains is generally the easiest appr...