IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v429y2015icp1-9.html
   My bibliography  Save this article

On a nonstandard Brownian motion and its maximal function

Author

Listed:
  • Andrade, Bernardo B. de

Abstract

This article uses Radically Elementary Probability Theory (REPT) to prove results about the Wiener walk (the radically elementary Brownian motion) without the technical apparatus required by stochastic integration. The techniques used replace measure-theoretic tools by discrete probability and the rigorous use of infinitesimals. Specifically, REPT is applied to the results in Palacios (The American Statistician, 2008) to calculate certain expectations related to the Wiener walk and its maximal function. Because Palacios uses mostly combinatorics and no measure theory his results carry over through REPT with minimal changes. The paper also presents a construction of the Wiener walk which is intended to mimic the construction of Brownian motion from “continuous” white noise. A brief review of the nonstandard model on which REPT is based is given in the Appendix in order to minimize the need for previous exposure to the subject.

Suggested Citation

  • Andrade, Bernardo B. de, 2015. "On a nonstandard Brownian motion and its maximal function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 429(C), pages 1-9.
    • Handle: RePEc:eee:phsmap:v:429:y:2015:i:c:p:1-9
    DOI: 10.1016/j.physa.2015.01.066
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437115000850
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2015.01.066?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Palacios, Jose Luis, 2008. "On the Simple Symmetric Random Walk and its Maximal Function," The American Statistician, American Statistical Association, vol. 62, pages 138-140, May.
    2. Robert N. Horn, 1988. "Analysis," Challenge, Taylor & Francis Journals, vol. 31(4), pages 56-58, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gilligan, Daniel O., 1998. "Farm Size, Productivity, And Economic Efficiency: Accounting For Differences In Efficiency Of Farms By Size In Honduras," 1998 Annual meeting, August 2-5, Salt Lake City, UT 20918, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    2. García, V.J. & Gómez-Déniz, E. & Vázquez-Polo, F.J., 2010. "A new skew generalization of the normal distribution: Properties and applications," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 2021-2034, August.
    3. Susanto Basu & John Fernald, 2001. "Why Is Productivity Procyclical? Why Do We Care?," NBER Chapters, in: New Developments in Productivity Analysis, pages 225-302, National Bureau of Economic Research, Inc.
    4. Kim, C.S. & Hallahan, Charles B. & Schaible, Glenn D. & Leath, Mack N., 2000. "A Decomposed Regression Model For Measuring Structural Changes In The Flour Milling Industry," 2000 Annual meeting, July 30-August 2, Tampa, FL 21834, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    5. Wei Chi & Richard B. Freeman & Morris M. Kleiner, 2011. "Adoption and Termination of Employee Involvement Programs," LABOUR, CEIS, vol. 25(1), pages 45-62, March.
    6. Harrison, Ann, 1996. "Openness and growth: A time-series, cross-country analysis for developing countries," Journal of Development Economics, Elsevier, vol. 48(2), pages 419-447, March.
    7. Pan, Shihua, 1990. "The microfoundations of mixed system of planning and markets: some theoretical considerations and an empirical analysis of the Chinese agriculture," ISU General Staff Papers 1990010108000010876, Iowa State University, Department of Economics.
    8. Robert G. Chambers & Erik Lichtenberg, 1994. "Simple Econometrics of Pesticide Productivity," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 76(3), pages 407-417.
    9. David I. Stern, 2012. "Interfuel Substitution: A Meta‐Analysis," Journal of Economic Surveys, Wiley Blackwell, vol. 26(2), pages 307-331, April.
    10. Giorgio Barba Navaretti & Riccardo Faini & Bernard Gauthier, 2006. "The Impact of Trade Liberalization on Enterprises in Small Backward Economies: the Case of Chad and Gabon," Review of Development Economics, Wiley Blackwell, vol. 10(3), pages 452-465, August.
    11. Judith Dean, 1995. "From protectionism to free trade fever? Recent reforms in developing countries," Open Economies Review, Springer, vol. 6(4), pages 369-385, October.
    12. Fullerton, Don & Karayannis, Marios, 1994. "Tax evasion and the allocation of capital," Journal of Public Economics, Elsevier, vol. 55(2), pages 257-278, October.
    13. Alejandro Plastina & Lilyan Fulginiti, 2012. "Rates of return to public agricultural research in 48 US states," Journal of Productivity Analysis, Springer, vol. 37(2), pages 95-113, April.
    14. Gebhardt Flaig & Horst Rottmann, 2001. "Input Demand and the Short‐ and Long‐Run Employment Thresholds: An Empirical Analysis for the German Manufacturing Sector," German Economic Review, Verein für Socialpolitik, vol. 2(4), pages 367-384, November.
    15. Patric H. Hendershott & Yunhi Won, 1991. "The Long-Run Impact on Federal Tax Revenues and Capital Allocation of a Cut in the Capital Gains Tax Rate," Public Finance Review, , vol. 19(1), pages 3-21, January.
    16. Blomstrom, Magnus & Fors, Gunnar & Lipsey, Robert E, 1997. "Foreign Direct Investment and Employment: Home Country Experience in the United States and Sweden," Economic Journal, Royal Economic Society, vol. 107(445), pages 1787-1797, November.
    17. Gian Paolo Barbetta & Gilberto Turati & Angelo M. Zago, 2007. "Behavioral differences between public and private not‐for‐profit hospitals in the Italian national health service," Health Economics, John Wiley & Sons, Ltd., vol. 16(1), pages 75-96, January.
    18. Perloff, Jeffrey M, 1991. "Econometric analysis of imperfect competition and implications for trade research," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt46w1j22d, Department of Agricultural & Resource Economics, UC Berkeley.
    19. Sergio H. Lence & Dermot J. Hayes, 2002. "U.S. Farm Policy and the Volatility of Commodity Prices and Farm Revenues," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 84(2), pages 335-351.
    20. Regier, Gregory K & Dalton, Timothy J, 2014. "Labour savings of Roundup Ready maize: Impact on cost and input substitution for South African smallholders," African Journal of Agricultural and Resource Economics, African Association of Agricultural Economists, vol. 9(3), pages 1-14, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:429:y:2015:i:c:p:1-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.