IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v201y2024i2d10.1007_s10957-024-02387-5.html
   My bibliography  Save this article

Dynamic Programming of the Stochastic Burgers Equation Driven by Lévy Noise

Author

Listed:
  • Manil T. Mohan

    (Indian Institute of Technology Roorkee-IIT Roorkee)

  • Kumarasamy Sakthivel

    (Indian Institute of Space Science and Technology (IIST))

  • Sivaguru S. Sritharan

    (National Academies/AFRL)

Abstract

In this work, we study the optimal control of stochastic Burgers equation perturbed by Gaussian and Lévy-type noises with distributed control process acting on the state equation. We use dynamic programming approach for the feedback synthesis to obtain an infinite-dimensional second-order Hamilton–Jacobi–Bellman (HJB) equation consisting of an integro-differential operator with Lévy measure associated with the stochastic control problem. Using the regularizing properties of the transition semigroup corresponding to the stochastic Burgers equation and compactness arguments, we solve the HJB equation and the resultant feedback control problem.

Suggested Citation

  • Manil T. Mohan & Kumarasamy Sakthivel & Sivaguru S. Sritharan, 2024. "Dynamic Programming of the Stochastic Burgers Equation Driven by Lévy Noise," Journal of Optimization Theory and Applications, Springer, vol. 201(2), pages 490-538, May.
    • Handle: RePEc:spr:joptap:v:201:y:2024:i:2:d:10.1007_s10957-024-02387-5
    DOI: 10.1007/s10957-024-02387-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-024-02387-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-024-02387-5?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. de Acosta, A., 1994. "Large deviations for vector-valued Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 51(1), pages 75-115, June.
    2. Giorgio Fabbri & Fausto Gozzi & Andrzej Swiech, 2017. "Stochastic Optimal Control in Infinite Dimensions - Dynamic Programming and HJB Equations," Post-Print hal-01505767, HAL.
    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. Macci, Claudio & Pacchiarotti, Barbara, 2015. "Large deviations for a class of counting processes and some statistical applications," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 36-48.
    2. Yongzhao Shao & Raúl Jiménez, 1998. "Entropy for Random Partitions and Its Applications," Journal of Theoretical Probability, Springer, vol. 11(2), pages 417-433, April.
    3. Masiero, Federica & Orrieri, Carlo & Tessitore, Gianmario & Zanco, Giovanni, 2021. "Semilinear Kolmogorov equations on the space of continuous functions via BSDEs," Stochastic Processes and their Applications, Elsevier, vol. 136(C), pages 1-56.
    4. Yan, Tingjin & Chiu, Mei Choi & Wong, Hoi Ying, 2023. "Portfolio liquidation with delayed information," Economic Modelling, Elsevier, vol. 126(C).
    5. Raouf Boucekkine & Giorgio Fabbri & Salvatore Federico & Fausto Gozzi, 2019. "Growth and agglomeration in the heterogeneous space: a generalized AK approach," Journal of Economic Geography, Oxford University Press, vol. 19(6), pages 1287-1318.
    6. Emmanuelle Augeraud-Véron & Raouf Boucekkine & Vladimir Veliov, 2019. "Distributed Optimal Control Models in Environmental Economics: A Review," Working Papers halshs-01982243, HAL.
    7. Dembo, Amir & Zajic, Tim, 1995. "Large deviations: From empirical mean and measure to partial sums process," Stochastic Processes and their Applications, Elsevier, vol. 57(2), pages 191-224, June.
    8. Fausto Gozzi & Federica Masiero & Mauro Rosestolato, 2024. "An optimal advertising model with carryover effect and mean field terms," Mathematics and Financial Economics, Springer, volume 18, number 9, October.
    9. Boucekkine, Raouf & Fabbri, Giorgio & Federico, Salvatore & Gozzi, Fausto, 2022. "A dynamic theory of spatial externalities," Games and Economic Behavior, Elsevier, vol. 132(C), pages 133-165.
    10. Jorge Garcia, 2008. "A Large Deviation Principle for Stochastic Integrals," Journal of Theoretical Probability, Springer, vol. 21(2), pages 476-501, June.
    11. Faggian, Silvia & Gozzi, Fausto & Kort, Peter M., 2021. "Optimal investment with vintage capital: Equilibrium distributions," Journal of Mathematical Economics, Elsevier, vol. 96(C).
    12. Adrien Genin & Peter Tankov, 2016. "Optimal importance sampling for L\'evy Processes," Papers 1608.04621, arXiv.org.
    13. Georgii Riabov & Aleh Tsyvinski, 2021. "Policy with stochastic hysteresis," Papers 2104.10225, arXiv.org.
    14. Briand, Philippe & Cardaliaguet, Pierre & Chaudru de Raynal, Paul-Éric & Hu, Ying, 2020. "Forward and backward stochastic differential equations with normal constraints in law," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7021-7097.
    15. Daras, Tryfon, 1998. "Trajectories of exchangeable sequences: Large and moderate deviations results," Statistics & Probability Letters, Elsevier, vol. 39(4), pages 289-304, August.
    16. Giorgio Fabbri & Francesco Russo, 2017. "HJB equations in infinite dimension and optimal control of stochastic evolution equations via generalized Fukushima decomposition," LIDAM Discussion Papers IRES 2017003, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    17. Baltas, I. & Dopierala, L. & Kolodziejczyk, K. & Szczepański, M. & Weber, G.-W. & Yannacopoulos, A.N., 2022. "Optimal management of defined contribution pension funds under the effect of inflation, mortality and uncertainty," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1162-1174.
    18. Michele Giordano & Anton Yurchenko-Tytarenko, 2024. "Optimal control in linear-quadratic stochastic advertising models with memory," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 47(1), pages 275-298, June.
    19. Michel Mandjes, 2022. "Multivariate M/G/1 systems with coupled input and parallel service," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 309-311, April.
    20. Paulwin Graewe & Ulrich Horst & Eric S'er'e, 2013. "Smooth solutions to portfolio liquidation problems under price-sensitive market impact," Papers 1309.0474, arXiv.org, revised Jun 2017.

    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:spr:joptap:v:201:y:2024:i:2:d:10.1007_s10957-024-02387-5. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.