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Journal articles on the topic 'Monte Carlo method'

Author: Grafiati

Published: 4 June 2021

Last updated: 12 October 2024

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1

Caflisch, Russel E. "Monte Carlo and quasi-Monte Carlo methods." Acta Numerica 7 (January 1998): 1–49. http://dx.doi.org/10.1017/s0962492900002804.

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Monte Carlo is one of the most versatile and widely used numerical methods. Its convergence rate, O(N−1/2), is independent of dimension, which shows Monte Carlo to be very robust but also slow. This article presents an introduction to Monte Carlo methods for integration problems, including convergence theory, sampling methods and variance reduction techniques. Accelerated convergence for Monte Carlo quadrature is attained using quasi-random (also called low-discrepancy) sequences, which are a deterministic alternative to random or pseudo-random sequences. The points in a quasi-random sequence are correlated to provide greater uniformity. The resulting quadrature method, called quasi-Monte Carlo, has a convergence rate of approximately O((logN)kN−1). For quasi-Monte Carlo, both theoretical error estimates and practical limitations are presented. Although the emphasis in this article is on integration, Monte Carlo simulation of rarefied gas dynamics is also discussed. In the limit of small mean free path (that is, the fluid dynamic limit), Monte Carlo loses its effectiveness because the collisional distance is much less than the fluid dynamic length scale. Computational examples are presented throughout the text to illustrate the theory. A number of open problems are described.

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2

Makarova, K. V., A. G. Makarov, M. A. Padalko, V. S. Strongin, and K. V. Nefedev. "Multispin Monte Carlo Method." Dal'nevostochnyi Matematicheskii Zhurnal 20, no. 2 (November 25, 2020): 212–20. http://dx.doi.org/10.47910/femj202020.

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The article offers a Monte Carlo cluster method for numerically calculating a statistical sample of the state space of vector models. The statistical equivalence of subsystems in the Ising model and quasi-Markov random walks can be used to increase the efficiency of the algorithm for calculating thermodynamic means. The cluster multispin approach extends the computational capabilities of the Metropolis algorithm and allows one to find configurations of the ground and low-energy states.

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3

Rajabalinejad, M. "Bayesian Monte Carlo method." Reliability Engineering & System Safety 95, no. 10 (October 2010): 1050–60. http://dx.doi.org/10.1016/j.ress.2010.04.014.

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4

The Lam, Nguyen. "QUANTUM DIFFUSION MONTE CARLO METHOD FOR LOW-DIMENTIONAL SYSTEMS." Journal of Science, Natural Science 60, no. 7 (2015): 81–87. http://dx.doi.org/10.18173/2354-1059.2015-0036.

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5

Siyamah, Imroatus, Endah RM Putri, and Chairul Imron. "Cat bond valuation using Monte Carlo and quasi Monte Carlo method." Journal of Physics: Conference Series 1821, no. 1 (March 1, 2021): 012053. http://dx.doi.org/10.1088/1742-6596/1821/1/012053.

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6

Kandidov, V. P. "Monte Carlo method in nonlinear statistical optics." Uspekhi Fizicheskih Nauk 166, no. 12 (1996): 1309. http://dx.doi.org/10.3367/ufnr.0166.199612c.1309.

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7

Rashki, Mohsen. "The soft Monte Carlo method." Applied Mathematical Modelling 94 (June 2021): 558–75. http://dx.doi.org/10.1016/j.apm.2021.01.022.

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8

Aboughantous, Charles H. "A Contributorn Monte Carlo Method." Nuclear Science and Engineering 118, no. 3 (November 1994): 160–77. http://dx.doi.org/10.13182/nse94-a19382.

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9

Bruce, A. D., A. N. Jackson, G. J. Ackland, and N. B. Wilding. "Lattice-switch Monte Carlo method." Physical Review E 61, no. 1 (January 1, 2000): 906–19. http://dx.doi.org/10.1103/physreve.61.906.

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10

Gubernatis, Jim, and Naomichi Hatano. "The multicanonical Monte Carlo method." Computing in Science & Engineering 2, no. 2 (March 2000): 95–102. http://dx.doi.org/10.1109/mcise.2000.5427643.

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11

Janke, Wolfhard, and Tilman Sauer. "Multicanonical multigrid Monte Carlo method." Physical Review E 49, no. 4 (April 1, 1994): 3475–79. http://dx.doi.org/10.1103/physreve.49.3475.

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12

Ohta, Shigemi. "Self-Test Monte Carlo Method." Progress of Theoretical Physics Supplement 122 (1996): 193–200. http://dx.doi.org/10.1143/ptps.122.193.

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13

Wang, Jian-Sheng. "Flat Histogram Monte Carlo Method." Progress of Theoretical Physics Supplement 138 (2000): 454–55. http://dx.doi.org/10.1143/ptps.138.454.

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14

Beichl, I., and F. Sullivan. "The other Monte Carlo method." Computing in Science & Engineering 8, no. 2 (March 2006): 42–47. http://dx.doi.org/10.1109/mcse.2006.35.

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15

Wang, Jian-Sheng. "Flat histogram Monte Carlo method." Physica A: Statistical Mechanics and its Applications 281, no. 1-4 (June 2000): 147–50. http://dx.doi.org/10.1016/s0378-4371(00)00016-9.

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16

Wang, Jian-Sheng. "Transition matrix Monte Carlo method." Computer Physics Communications 121-122 (September 1999): 22–25. http://dx.doi.org/10.1016/s0010-4655(99)00270-2.

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17

Schaefer, G., and P. Hui. "The Monte Carlo flux method." Journal of Computational Physics 89, no. 1 (July 1990): 1–30. http://dx.doi.org/10.1016/0021-9991(90)90114-g.

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18

Ray, John R. "Microcanonical ensemble Monte Carlo method." Physical Review A 44, no. 6 (September 1, 1991): 4061–64. http://dx.doi.org/10.1103/physreva.44.4061.

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19

Oht, Shigemi. "Self-test Monte Carlo method." Nuclear Physics B - Proceedings Supplements 47, no. 1-3 (March 1996): 788–91. http://dx.doi.org/10.1016/0920-5632(96)00175-2.

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20

Towler, M. D. "The quantum Monte Carlo method." physica status solidi (b) 243, no. 11 (August 21, 2006): 2573–98. http://dx.doi.org/10.1002/pssb.200642125.

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21

Lee, Jin-Han, Young-Do Jo, and Lae Hyun Kim. "Reliability Assessment for Corroded Pipelines by Separable Monte Carlo Method." Journal of the Korean Institute of Gas 19, no. 5 (October 30, 2015): 81–86. http://dx.doi.org/10.7842/kigas.2015.19.5.81.

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22

Puddu, G. "A comparison between the Monte Carlo shell model method and the Monte Carlo spectroscopic method." Journal of Physics G: Nuclear and Particle Physics 29, no. 9 (July 28, 2003): 2179–85. http://dx.doi.org/10.1088/0954-3899/29/9/312.

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23

Giles, Michael B. "Multilevel Monte Carlo methods." Acta Numerica 24 (April 27, 2015): 259–328. http://dx.doi.org/10.1017/s096249291500001x.

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Monte Carlo methods are a very general and useful approach for the estimation of expectations arising from stochastic simulation. However, they can be computationally expensive, particularly when the cost of generating individual stochastic samples is very high, as in the case of stochastic PDEs. Multilevel Monte Carlo is a recently developed approach which greatly reduces the computational cost by performing most simulations with low accuracy at a correspondingly low cost, with relatively few simulations being performed at high accuracy and a high cost.In this article, we review the ideas behind the multilevel Monte Carlo method, and various recent generalizations and extensions, and discuss a number of applications which illustrate the flexibility and generality of the approach and the challenges in developing more efficient implementations with a faster rate of convergence of the multilevel correction variance.

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24

SIKORSKI, ANDRZEJ. "Method of Monte Carlo entropy sampling in polymer SYSTEMS." Polimery 45, no. 07/08 (July 2000): 514–19. http://dx.doi.org/10.14314/polimery.2000.514.

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25

Shymanska, Alla V., and Vitali A. Babakov. "Fast Monte Carlo Method in Stochastic Modelling of Charged Particle Multiplication." International Journal of Applied Physics and Mathematics 5, no. 3 (2015): 218–26. http://dx.doi.org/10.17706/ijapm.2015.5.3.218-226.

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26

Betancourt, Michael. "The Convergence of Markov Chain Monte Carlo Methods: From the Metropolis Method to Hamiltonian Monte Carlo." Annalen der Physik 531, no. 3 (March 23, 2018): 1700214. http://dx.doi.org/10.1002/andp.201700214.

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27

NIEDERREITER, HARALD. "QUASI-MONTE CARLO METHODS IN COMPUTATIONAL FINANCE." COSMOS 01, no. 01 (May 2005): 113–25. http://dx.doi.org/10.1142/s0219607705000097.

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Quasi-Monte Carlo methods are deterministic versions of Monte Carlo methods, in the sense that the random samples used in the implementation of a Monte Carlo method are replaced by judiciously chosen deterministic points with good distribution properties. They outperform classical Monte Carlo methods in many problems of scientific computing. This paper discusses applications of quasi-Monte Carlo methods to computational finance, with a special emphasis on the problems of pricing mortgage-backed securities and options. The necessary background on Monte Carlo and quasi-Monte Carlo methods is also provided.

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28

Ohtani, Yoshihiko, Mamoru Ohkawa, Akira Uchida, and Tetsuo Yamaya. "Illuminance Calculation Using Monte Carlo Method." JOURNAL OF THE ILLUMINATING ENGINEERING INSTITUTE OF JAPAN 82, no. 2 (1998): 105–11. http://dx.doi.org/10.2150/jieij1980.82.2_105.

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29

Wenger, Trey V., Dana S. Balser, L. D. Anderson, and T. M. Bania. "Kinematic Distances: A Monte Carlo Method." Astrophysical Journal 856, no. 1 (March 23, 2018): 52. http://dx.doi.org/10.3847/1538-4357/aaaec8.

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30

Ranjbaran, Abdolrasoul, Mohammad Ranjbaran, and Fatema Ranjbaran. "Persian Curve Versus Monte Carlo Method." International Journal of Structural Glass and Advanced Materials Research 5, no. 1 (January 1, 2021): 234–46. http://dx.doi.org/10.3844/sgamrsp.2021.234.246.

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31

Takahashi, Akihiko, and Nakahiro Yoshida. "Monte Carlo Simulation with Asymptotic Method." JOURNAL OF THE JAPAN STATISTICAL SOCIETY 35, no. 2 (2005): 171–203. http://dx.doi.org/10.14490/jjss.35.171.

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32

Alexander, Francis J., and Alejandro L. Garcia. "The Direct Simulation Monte Carlo Method." Computers in Physics 11, no. 6 (1997): 588. http://dx.doi.org/10.1063/1.168619.

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33

OHTANI, Yoshihiko, Mamoru OHKAWA, Akira UCHIDA, and Tetsuo YAMAYA. "Illuminance Calculation Using Monte Carlo Method." Journal of Light & Visual Environment 24, no. 1 (2000): 42–49. http://dx.doi.org/10.2150/jlve.24.1_42.

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34

Bokor, Nandor. "Monte Carlo method in computer holography." Optical Engineering 36, no. 4 (April 1, 1997): 1014. http://dx.doi.org/10.1117/1.601294.

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35

Lacasse, Martin-D., Jorge Viñals, and Martin Grant. "Dynamic Monte Carlo renormalization-group method." Physical Review B 47, no. 10 (March 1, 1993): 5646–52. http://dx.doi.org/10.1103/physrevb.47.5646.

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36

Kröger, Helmut. "Monte Carlo method for scattering reactions." Physical Review A 35, no. 11 (June 1, 1987): 4526–32. http://dx.doi.org/10.1103/physreva.35.4526.

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37

Jones, Matthew D., Gerardo Ortiz, and David M. Ceperley. "Released-phase quantum Monte Carlo method." Physical Review E 55, no. 5 (May 1, 1997): 6202–10. http://dx.doi.org/10.1103/physreve.55.6202.

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38

Iskandar, S. "Modified Monte Carlo method for integral." Journal of Physics: Conference Series 1462 (February 2020): 012061. http://dx.doi.org/10.1088/1742-6596/1462/1/012061.

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39

Fernández, L. A., V. Martín-Mayor, and P. Verrocchio. "Optimized Monte Carlo method for glasses." Philosophical Magazine 87, no. 3-5 (January 21, 2007): 581–86. http://dx.doi.org/10.1080/14786430600919302.

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40

Berg, B., A. Billoire, and D. Foerster. "Monte Carlo method for random surfaces." Nuclear Physics B 251 (January 1985): 665–75. http://dx.doi.org/10.1016/s0550-3213(85)80002-x.

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41

de Lataillade, A., S. Blanco, Y. Clergent, J. L. Dufresne, M. El Hafi, and R. Fournier. "Monte Carlo method and sensitivity estimations." Journal of Quantitative Spectroscopy and Radiative Transfer 75, no. 5 (December 2002): 529–38. http://dx.doi.org/10.1016/s0022-4073(02)00027-4.

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42

Rota, Gian-Carlo. "Simulation and the Monte-Carlo method." Advances in Mathematics 60, no. 1 (April 1986): 123. http://dx.doi.org/10.1016/0001-8708(86)90009-5.

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43

Gupta, Rajan, K. G. Wilson, and C. Umrigar. "Improved Monte Carlo renormalization group method." Journal of Statistical Physics 43, no. 5-6 (June 1986): 1095–99. http://dx.doi.org/10.1007/bf02628333.

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44

Socha, J. B., and J. A. Krumhansl. "The Monte Carlo trajectory integral method." Physica B+C 134, no. 1-3 (November 1985): 142–47. http://dx.doi.org/10.1016/0378-4363(85)90334-1.

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45

Mackenze, Paul B. "An improved hybrid Monte Carlo method." Physics Letters B 226, no. 3-4 (August 1989): 369–71. http://dx.doi.org/10.1016/0370-2693(89)91212-4.

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46

Date, Hiroyuki. "1. Principle of Monte Carlo Method." Japanese Journal of Radiological Technology 70, no. 6 (2014): 582–87. http://dx.doi.org/10.6009/jjrt.2014_jsrt_70.6.582.

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47

Date, Hiroyuki. "2. Monte Carlo Method and Simulation." Japanese Journal of Radiological Technology 70, no. 7 (2014): 705–14. http://dx.doi.org/10.6009/jjrt.2014_jsrt_70.7.705.

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48

Goodman, Jonathan, and Alan D. Sokal. "Multigrid Monte Carlo method. Conceptual foundations." Physical Review D 40, no. 6 (September 15, 1989): 2035–71. http://dx.doi.org/10.1103/physrevd.40.2035.

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49

Care, C. M. "Rejection-free microcanonical Monte Carlo method." Journal of Physics A: Mathematical and General 29, no. 20 (October 21, 1996): L505—L509. http://dx.doi.org/10.1088/0305-4470/29/20/001.

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50

Prokhorov, A. V. "Monte Carlo method in optical radiometry." Metrologia 35, no. 4 (August 1998): 465–71. http://dx.doi.org/10.1088/0026-1394/35/4/44.

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