IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v130y2020i5p2974-3004.html
   My bibliography  Save this article

On Bernstein processes generated by hierarchies of linear parabolic systems in Rd

Author

Listed:
  • Vuillermot, Pierre-A.
  • Zambrini, J.-C.

Abstract

In this article we investigate the properties of Bernstein processes generated by infinite hierarchies of forward–backward systems of decoupled linear deterministic parabolic partial differential equations defined in Rd, where d is arbitrary. An important feature of those systems is that the elliptic part of the parabolic operators may be realized as an unbounded Schrödinger operator with compact resolvent in standard L2-space. The Bernstein processes we are interested in are in general non-Markovian, may be stationary or non-stationary and are generated by weighted averages of measures naturally associated with the pure point spectrum of the operator. We also introduce time-dependent trace-class operators which possess several attributes of density operators in Quantum Statistical Mechanics, and prove that the statistical averages of certain bounded self-adjoint observables usually evaluated by means of such operators coincide with the expectation values of suitable functions of the underlying processes. In the particular case where the given parabolic equations involve the Hamiltonian of an isotropic system of quantum harmonic oscillators, we show that one of the associated processes is identical in law with the periodic Ornstein–Uhlenbeck process.

Suggested Citation

  • Vuillermot, Pierre-A. & Zambrini, J.-C., 2020. "On Bernstein processes generated by hierarchies of linear parabolic systems in Rd," Stochastic Processes and their Applications, Elsevier, vol. 130(5), pages 2974-3004.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:5:p:2974-3004
    DOI: 10.1016/j.spa.2019.09.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414919300857
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2019.09.003?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. Alfred Galichon, 2016. "Optimal transport methods in economics," Post-Print hal-03256830, HAL.
    2. Alfred Galichon, 2016. "Optimal Transport Methods in Economics," Economics Books, Princeton University Press, edition 1, number 10870.
    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. Pablo D. Fajgelbaum & Edouard Schaal, 2020. "Optimal Transport Networks in Spatial Equilibrium," Econometrica, Econometric Society, vol. 88(4), pages 1411-1452, July.
    2. Carlier, Guillaume & Dupuy, Arnaud & Galichon, Alfred & Sun, Yifei, 2021. "SISTA: Learning Optimal Transport Costs under Sparsity Constraints," IZA Discussion Papers 14397, Institute of Labor Economics (IZA).
    3. Arthur Charpentier & Alfred Galichon & Lucas Vernet, 2019. "Optimal transport on large networks, a practitioner's guide," Papers 1907.02320, arXiv.org, revised Aug 2019.
    4. Odran Bonnet & Alfred Galichon & Yu-Wei Hsieh & Keith O’Hara & Matt Shum, 2022. "Yogurts Choose Consumers? Estimation of Random-Utility Models via Two-Sided Matching," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(6), pages 3085-3114.
    5. Francesca Molinari, 2020. "Microeconometrics with Partial Identi?cation," CeMMAP working papers CWP15/20, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. Adrien Bilal & Esteban Rossi‐Hansberg, 2021. "Location as an Asset," Econometrica, Econometric Society, vol. 89(5), pages 2459-2495, September.
    7. Alexander V. Kolesnikov & Fedor Sandomirskiy & Aleh Tsyvinski & Alexander P. Zimin, 2022. "Beckmann's approach to multi-item multi-bidder auctions," Papers 2203.06837, arXiv.org, revised Sep 2022.
    8. Arthur Charpentier & Emmanuel Flachaire & Ewen Gallic, 2023. "Optimal Transport for Counterfactual Estimation: A Method for Causal Inference," Papers 2301.07755, arXiv.org.
    9. Alfred Galichon & Bernard Salani'e, 2021. "Cupid's Invisible Hand: Social Surplus and Identification in Matching Models," Papers 2106.02371, arXiv.org, revised Jan 2023.
    10. Florian Gunsilius & Susanne M. Schennach, 2017. "A nonlinear principal component decomposition," CeMMAP working papers 16/17, Institute for Fiscal Studies.
    11. Sergio Ocampo, 2019. "A task-based theory of occupations with multidimensional heterogeneity," 2019 Meeting Papers 477, Society for Economic Dynamics.
    12. Mario Ghossoub & David Saunders, 2020. "On the Continuity of the Feasible Set Mapping in Optimal Transport," Papers 2009.12838, arXiv.org.
    13. Itai Arieli & Yakov Babichenko & Fedor Sandomirskiy, 2023. "Feasible Conditional Belief Distributions," Papers 2307.07672, arXiv.org, revised Nov 2024.
    14. Brendan Pass, 2019. "Interpolating between matching and hedonic pricing models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(2), pages 393-419, March.
    15. Mario Ghossoub & David Saunders, 2021. "On the continuity of the feasible set mapping in optimal transport," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(1), pages 113-117, April.
    16. Walter W. Zhang & Sanjog Misra, 2022. "Coarse Personalization," Papers 2204.05793, arXiv.org, revised Aug 2024.
    17. Salanié, Bernard & Chiappori, Pierre-André, 2021. "Mating Markets," CEPR Discussion Papers 16041, C.E.P.R. Discussion Papers.
      • Pierre-André Chiappori & Bernard Salanié, 2021. "Mating Markets," Working Papers 2021-016, Human Capital and Economic Opportunity Working Group.
    18. Florian Gunsilius, 2018. "Point-identification in multivariate nonseparable triangular models," Papers 1806.09680, arXiv.org.
    19. Fally, Thibault & Hillberry, Russell, 2018. "A Coasian model of international production chains," Journal of International Economics, Elsevier, vol. 114(C), pages 299-315.
    20. Andrew Lyasoff, 2023. "Self-Aware Transport of Economic Agents," Papers 2303.12567, arXiv.org, revised Aug 2024.

    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:eee:spapps:v:130:y:2020:i:5:p:2974-3004. 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.