New Monte Carlo algorithms for investigation of criticality fluctuations in the particle scattering process with multiplication in stochastic media

2017 ◽  
Vol 32 (3) ◽  
Author(s):  
Andrey Yu. Ambos ◽  
Galiya Lotova ◽  
Guennady Mikhailov
Keyword(s):  
Monte Carlo ◽  
Random Medium ◽  
Homogenization Method ◽  
Monte Carlo Algorithm ◽  
Symmetric Model ◽  
Small Perturbations ◽  
Monte Carlo Algorithms ◽  
Stochastic Media ◽  
Diffusive Approximation ◽  
Spherically Symmetric Model

AbstractA Monte Carlo algorithm admitting parallelization is constructed for estimation of probability moments of the spectral radius of the operator of the integral equation describing transfer of particles with multiplication in a random medium. A randomized homogenization method is developed with the same aim on the base of the theory of small perturbations and diffusive approximation. Test calculations performed for a one-group spherically symmetric model system have shown a satisfactory concordance of results obtained from two models.

Convergence Properties of Perturbed Markov Chains

1998 ◽  
Vol 35 (01) ◽  
pp. 1-11 ◽  
Author(s):  
Gareth O. Roberts ◽  
Jeffrey S. Rosenthal ◽  
Peter O. Schwartz
Keyword(s):  
Computer Simulation ◽  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chains ◽  
Rates Of Convergence ◽  
Geometric Ergodicity ◽  
Roundoff Error ◽  
Convergence Properties ◽  
Small Perturbations ◽  
Monte Carlo Algorithms

In this paper, we consider the question of which convergence properties of Markov chains are preserved under small perturbations. Properties considered include geometric ergodicity and rates of convergence. Perturbations considered include roundoff error from computer simulation. We are motivated primarily by interest in Markov chain Monte Carlo algorithms.

LOCALIZED MONTE CARLO ALGORITHM TO COMPUTE PRICES OF PATH DEPENDENT OPTIONS ON TREES

2005 ◽  
Vol 08 (05) ◽  
pp. 553-574 ◽  
Author(s):  
SEBASTIAN E. FERRANDO ◽  
ARIEL J. BERNAL
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Algorithm ◽  
European Options ◽  
General Applicability ◽  
Underlying Process ◽  
Monte Carlo Algorithms ◽  
Simulation Based ◽  
Path Dependent ◽  
Probabilistic Error

A new simulation based algorithm to approximate prices of path dependent European options is introduced. The algorithm is defined for tree-like approximations to the underlying process and makes extensive use of structural properties of the discrete approximation. We indicate the advantages of the new algorithm in comparison to standard Monte Carlo algorithms. In particular, we prove a probabilistic error bound that compares the quality of both approximations. The algorithm is of general applicability and, for a large class of options, it has the same computational complexity as Monte Carlo.

A diffusion Monte Carlo method for charge density on a conducting surface at non-constant potentials

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Unjong Yu ◽  
Hoseung Jang ◽  
Chi-Ok Hwang
Keyword(s):  
Monte Carlo ◽  
Charge Density ◽  
Potential Surface ◽  
Circular Disk ◽  
Monte Carlo Algorithm ◽  
Conducting Surface ◽  
Charge Densities ◽  
Monte Carlo Algorithms ◽  
Constant Potential ◽  
Diffusion Monte Carlo Method

Abstract We develop a last-passage Monte Carlo algorithm on a conducting surface at non-constant potentials. In the previous researches, last-passage Monte Carlo algorithms on conducting surfaces with a constant potential have been developed for charge density at a specific point or on a finite region and a hybrid BIE-WOS algorithm for charge density on a conducting surface at non-constant potentials. In the hybrid BIE-WOS algorithm, they used a deterministic method for the contribution from the lower non-constant potential surface. In this paper, we modify the hybrid BIE-WOS algorithm to a last-passage Monte Carlo algorithm on a conducting surface at non-constant potentials, where we can avoid the singularities on the non-constant potential surface very naturally. We demonstrate the last-passage Monte Carlo algorithm for charge densities on a circular disk and the four rectangle plates with a simple voltage distribution, and update the corner singularities on the unit square plate and cube.

scholarly journals Extended stochastic gradient Markov chain Monte Carlo for large-scale Bayesian variable selection

Biometrika ◽  
2020 ◽  
Vol 107 (4) ◽  
pp. 997-1004
Author(s):  
Qifan Song ◽  
Yan Sun ◽  
Mao Ye ◽  
Faming Liang
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Latent Variables ◽  
Large Scale ◽  
Bayesian Variable Selection ◽  
Stochastic Gradient ◽  
Monte Carlo Algorithm ◽  
Monte Carlo Algorithms ◽  
Fixed Dimension

Summary Stochastic gradient Markov chain Monte Carlo algorithms have received much attention in Bayesian computing for big data problems, but they are only applicable to a small class of problems for which the parameter space has a fixed dimension and the log-posterior density is differentiable with respect to the parameters. This paper proposes an extended stochastic gradient Markov chain Monte Carlo algorithm which, by introducing appropriate latent variables, can be applied to more general large-scale Bayesian computing problems, such as those involving dimension jumping and missing data. Numerical studies show that the proposed algorithm is highly scalable and much more efficient than traditional Markov chain Monte Carlo algorithms.

scholarly journals Generalised Sifting in Black-Box Groups

2005 ◽  
Vol 8 ◽  
pp. 217-250
Author(s):  
Sophie Ambrose ◽  
Max Neunhöffer ◽  
Cheryl E. Praeger ◽  
Csaba Schneider
Keyword(s):  
Monte Carlo ◽  
Black Box ◽  
Monte Carlo Algorithm ◽  
Simple Groups ◽  
Sporadic Groups ◽  
Major Objective ◽  
Monte Carlo Algorithms ◽  
Sporadic Simple Groups ◽  
Computational Procedures ◽  
A Chain

AbstractThis paper presents a generalisation of the sifting procedure introduced originally by Sims for computation with finite permutation groups, and now used for many computational procedures for groups, such as membership testing and finding group orders. The new procedure is a Monte Carlo algorithm, and it is presented and analysed in the context of black-box groups. It is based on a chain of subsets instead of a subgroup chain. Two general versions of the procedure are worked out in detail, and applications are given for membership tests for several of the sporadic simple groups. The authors' major objective was that the procedures could be proved to be Monte Carlo algorithms, and the costs computed. In addition, they explicitly determined suitable subset chains for six of the sporadic groups, and then implemented the algorithms involving these chains in the GAP computational algebra system. It turns out that sample imple-mentations perform well in practice. The implementations will be made available publicly in the form of a GAP package.

Convergence Properties of Perturbed Markov Chains

1998 ◽  
Vol 35 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Gareth O. Roberts ◽  
Jeffrey S. Rosenthal ◽  
Peter O. Schwartz
Keyword(s):  
Computer Simulation ◽  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chains ◽  
Rates Of Convergence ◽  
Geometric Ergodicity ◽  
Roundoff Error ◽  
Convergence Properties ◽  
Small Perturbations ◽  
Monte Carlo Algorithms

In this paper, we consider the question of which convergence properties of Markov chains are preserved under small perturbations. Properties considered include geometric ergodicity and rates of convergence. Perturbations considered include roundoff error from computer simulation. We are motivated primarily by interest in Markov chain Monte Carlo algorithms.

scholarly journals ODD-FLAVOR HYBRID MONTE CARLO ALGORITHM FOR LATTICE QCD

2002 ◽  
Vol 13 (03) ◽  
pp. 343-365 ◽  
Author(s):  
TETSUYA TAKAISHI ◽  
PHILIPPE de FORCRAND
Keyword(s):  
Monte Carlo ◽  
Lattice Qcd ◽  
Correction Factor ◽  
Polynomial Approximation ◽  
Monte Carlo Algorithm ◽  
Hybrid Monte Carlo ◽  
Monte Carlo Algorithms

We discuss hybrid Monte Carlo algorithms for odd-flavor lattice QCD simulations. The algorithms include a polynomial approximation, which enables us to simulate odd-flavor QCD in the framework of the hybrid Monte Carlo algorithm. In order to make the algorithms exact, the correction factor to the polynomial approximation is also included in an economical, stochastic way. We test the algorithms for nf = 1, 1 + 1 and 2 + 1 flavors and compare results with other algorithms.

Monte Carlo Algorithms for Moments of Transition Arrays

1988 ◽  
Vol 102 ◽  
pp. 79-81
Author(s):  
A. Goldberg ◽  
S.D. Bloom
Keyword(s):  
Monte Carlo ◽  
State Vector ◽  
Basis Vector ◽  
Collective State ◽  
Dispersion Characteristics ◽  
Dipole Strength ◽  
The Third ◽  
Monte Carlo Algorithms ◽  
Third Moment ◽  
Very High

AbstractClosed expressions for the first, second, and (in some cases) the third moment of atomic transition arrays now exist. Recently a method has been developed for getting to very high moments (up to the 12th and beyond) in cases where a “collective” state-vector (i.e. a state-vector containing the entire electric dipole strength) can be created from each eigenstate in the parent configuration. Both of these approaches give exact results. Herein we describe astatistical(or Monte Carlo) approach which requires onlyonerepresentative state-vector |RV> for the entire parent manifold to get estimates of transition moments of high order. The representation is achieved through the random amplitudes associated with each basis vector making up |RV>. This also gives rise to the dispersion characterizing the method, which has been applied to a system (in the M shell) with≈250,000 lines where we have calculated up to the 5th moment. It turns out that the dispersion in the moments decreases with the size of the manifold, making its application to very big systems statistically advantageous. A discussion of the method and these dispersion characteristics will be presented.

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