IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v123y2013i1p191-211.html
   My bibliography  Save this article

The expected area of the Wiener sausage swept by a disc

Author

Listed:
  • Uchiyama, Kôhei

Abstract

The expected areas of the Wiener sausages swept by a disc attached to the two-dimensional Brownian Bridge joining the origin to a point x over a time interval [0,t] are computed. It is proved that the leading term of the expectation is given by Ramanujan’s function if |x|=O(t). The second term is also given explicitly when |x|=o(t). The corresponding result for unconditioned process is also obtained.

Suggested Citation

  • Uchiyama, Kôhei, 2013. "The expected area of the Wiener sausage swept by a disc," Stochastic Processes and their Applications, Elsevier, vol. 123(1), pages 191-211.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:1:p:191-211
    DOI: 10.1016/j.spa.2012.09.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414912001986
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2012.09.005?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. P. Frevert, 1971. "Note," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(2), pages 269-270.
    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. Rai, Birendra & Sengupta, Kunal, 2013. "Pre-marital confinement of women: A signaling and matching approach," Journal of Development Economics, Elsevier, vol. 105(C), pages 48-63.
    2. Snyder, Ralph D. & Ord, J. Keith & Beaumont, Adrian, 2012. "Forecasting the intermittent demand for slow-moving inventories: A modelling approach," International Journal of Forecasting, Elsevier, vol. 28(2), pages 485-496.
    3. Christina D. Romer & David Romer, 1999. "Monetary policy and the well-being of the poor," Economic Review, Federal Reserve Bank of Kansas City, vol. 84(Q I), pages 21-49.
    4. Rao Aiyagari, S., 1992. "Walras' Law and nonoptimal equilibria in overlapping generations models," Journal of Mathematical Economics, Elsevier, vol. 21(4), pages 343-361.
    5. Bowsher, Clive G., 2007. "Modelling security market events in continuous time: Intensity based, multivariate point process models," Journal of Econometrics, Elsevier, vol. 141(2), pages 876-912, December.
    6. Giovanna Bimonte & Maria Graziano, 2009. "The measure of blocking coalitions in differential information economies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(2), pages 331-350, February.
    7. Robert Winkler & Victor Jose, 2008. "Comments on: Assessing probabilistic forecasts of multivariate quantities, with an application to ensemble predictions of surface winds," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(2), pages 251-255, August.
    8. Katherine M. O'Regan & John M. Quigley, 1998. "Where Youth Live: Economic Effects of Urban Space on Employment Prospects," Urban Studies, Urban Studies Journal Limited, vol. 35(7), pages 1187-1205, June.
    9. Anne Evans & Nick Manning & Yasin Osmani & Anne Tully & Andrew Wilder, 2004. "A Guide to Government in Afghanistan," World Bank Publications - Books, The World Bank Group, number 14937.
    10. Frederic Schoenberg, 2002. "On Rescaled Poisson Processes and the Brownian Bridge," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(2), pages 445-457, June.
    11. Giada Adelfio & Frederic Schoenberg, 2009. "Point process diagnostics based on weighted second-order statistics and their asymptotic properties," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(4), pages 929-948, December.
    12. Robert J. Gordon, 1988. "U.S. Inflation, Labor's Share, and the Natural Rate of Unemployment," NBER Working Papers 2585, National Bureau of Economic Research, Inc.
    13. Beaumont, Adrian N., 2014. "Data transforms with exponential smoothing methods of forecasting," International Journal of Forecasting, Elsevier, vol. 30(4), pages 918-927.
    14. Roulston, M.S. & Kaplan, D.T. & Hardenberg, J. & Smith, L.A., 2003. "Using medium-range weather forcasts to improve the value of wind energy production," Renewable Energy, Elsevier, vol. 28(4), pages 585-602.
    15. Boero, Gianna & Smith, Jeremy & Wallis, Kenneth F., 2011. "Scoring rules and survey density forecasts," International Journal of Forecasting, Elsevier, vol. 27(2), pages 379-393.
    16. Robert J. Gordon & Arthur M. Okun & Herbert Stein, 1980. "Postwar Macroeconomics: The Evolution of Events and Ideas," NBER Chapters, in: The American Economy in Transition, pages 101-182, National Bureau of Economic Research, Inc.
    17. Alex Avilés & Rolando Célleri & Javier Paredes & Abel Solera, 2015. "Evaluation of Markov Chain Based Drought Forecasts in an Andean Regulated River Basin Using the Skill Scores RPS and GMSS," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(6), pages 1949-1963, April.
    18. Greenberg, Joseph & Weber, Shlomo & Yamazaki, Akira, 2007. "On blocking coalitions: Linking Mas-Colell with Grodal-Schmeidler-Vind," Journal of Mathematical Economics, Elsevier, vol. 43(5), pages 615-628, June.
    19. Schoenberg, Frederic, 1999. "Transforming spatial point processes into Poisson processes," Stochastic Processes and their Applications, Elsevier, vol. 81(2), pages 155-164, June.
    20. Wojciech Olszewski & Alvaro Sandroni, 2008. "Manipulability of Future-Independent Tests," Econometrica, Econometric Society, vol. 76(6), pages 1437-1466, November.

    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:spapps:v:123:y:2013:i:1:p:191-211. 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.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.