IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2404.00784.html
   My bibliography  Save this paper

Estimating sample paths of Gauss-Markov processes from noisy data

Author

Listed:
  • Benjamin Davies

Abstract

I derive the pointwise conditional means and variances of an arbitrary Gauss-Markov process, given noisy observations of points on a sample path. These moments depend on the process's mean and covariance functions, and on the conditional moments of the sampled points. I study the Brownian motion and bridge as special cases.

Suggested Citation

  • Benjamin Davies, 2024. "Estimating sample paths of Gauss-Markov processes from noisy data," Papers 2404.00784, arXiv.org.
    • Handle: RePEc:arx:papers:2404.00784
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2404.00784
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Benjamin Davies, 2024. "Learning about a changing state," Papers 2401.03607, arXiv.org.
    2. Steven Callander, 2011. "Searching and Learning by Trial and Error," American Economic Review, American Economic Association, vol. 101(6), pages 2277-2308, October.
    3. Christoph Carnehl & Johannes Schneider, 2021. "A Quest for Knowledge," Papers 2102.13434, arXiv.org, revised Aug 2023.
    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. Cujean, Julien & Bustamante, Maria Cecilia & Frésard, Laurent, 2019. "Knowledge Cycles and Corporate Investment," CEPR Discussion Papers 14152, C.E.P.R. Discussion Papers.
    2. Doruk Cetemen & Can Urgun & Leeat Yariv, 2023. "Collective Progress: Dynamics of Exit Waves," Journal of Political Economy, University of Chicago Press, vol. 131(9), pages 2402-2450.
    3. Ben Klemens, 2021. "Attributing Value to Patents and Trademarks in Complex Production Chains," Journal of the Knowledge Economy, Springer;Portland International Center for Management of Engineering and Technology (PICMET), vol. 12(2), pages 842-875, June.
    4. Anand, Kartik & Gai, Prasanna & König, Philipp Johann, 2020. "Leaping into the dark: A theory of policy gambles," Discussion Papers 07/2020, Deutsche Bundesbank.
    5. Morten Hertzum, 2023. "Information seeking by experimentation: Trying something out to discover what happens," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 74(4), pages 383-387, April.
    6. Maloney,William F. & Zambrano,Andrés, 2021. "Learning to Learn : Experimentation, Entrepreneurial Capital, and Development," Policy Research Working Paper Series 9890, The World Bank.
    7. Morelli, Massimo & Foarta, Dana, 2020. "Equilibrium Reforms and Endogenous Complexity," CEPR Discussion Papers 15136, C.E.P.R. Discussion Papers.
    8. Andreas Bernecker & Pierre C. Boyer & Christina Gathmann, 2021. "The Role of Electoral Incentives for Policy Innovation: Evidence from the US Welfare Reform," American Economic Journal: Economic Policy, American Economic Association, vol. 13(2), pages 26-57, May.
    9. Bernecker, Andreas & Boyer, Pierre C. & Gathmann, Christina, 2015. "Trial and Error? Reelection Concerns and Policy Experimentation during the U.S. Welfare Reform," IZA Discussion Papers 9113, Institute of Labor Economics (IZA).
    10. Serguey Braguinsky & Atsushi Ohyama & Tetsuji Okazaki & Chad Syverson, 2021. "Product Innovation, Product Diversification, and Firm Growth: Evidence from Japan's Early Industrialization," American Economic Review, American Economic Association, vol. 111(12), pages 3795-3826, December.
    11. Letina, Igor & Schmutzler, Armin & Seibel, Regina, 2020. "Killer Acquisitions and Beyond: Policy Effects on Innovation Strategies," CEPR Discussion Papers 15167, C.E.P.R. Discussion Papers.
    12. Umberto Garfagnini & Bruno Strulovici, 2012. "Social Learning and Innovation Cycles (revision of DP#1516, The Dynamics of Innovation)," Discussion Papers 1546, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    13. Ian R Turner, 2017. "Working smart and hard? Agency effort, judicial review, and policy precision," Journal of Theoretical Politics, , vol. 29(1), pages 69-96, January.
    14. Donald E. Bowen & Laurent Frésard & Gerard Hoberg, 2023. "Rapidly Evolving Technologies and Startup Exits," Management Science, INFORMS, vol. 69(2), pages 940-967, February.
    15. Peiran Jiao, 2015. "The Double-Channeled Effects of Experience on Individual Investment Decisions: Experimental Evidence," Economics Series Working Papers 766, University of Oxford, Department of Economics.
    16. Scott E Page & John Vandermeer, 2013. "Inequality and Innovativeness," Economics Bulletin, AccessEcon, vol. 33(1), pages 1-59.
    17. João V. Ferreira & Nicolas Gravel, 2017. "Choice with Time," AMSE Working Papers 1729, Aix-Marseille School of Economics, France.
    18. Baskaran, Thushyanthan, 2015. "Tax mimicking in the short- and long-run: Evidence from German reunification," University of Göttingen Working Papers in Economics 230, University of Goettingen, Department of Economics.
    19. Annie Liang & Xiaosheng Mu & Vasilis Syrgkanis, 2021. "Dynamically Aggregating Diverse Information," Working Papers 2021-43, Princeton University. Economics Department..
    20. Can Urgun & Leeat Yariv, 2021. "Retrospective Search: Exploration and Ambition on Uncharted Terrain," Working Papers 2021-33, Princeton University. Economics Department..

    More about this item

    Statistics

    Access and download statistics

    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:arx:papers:2404.00784. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.