IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v162y2023icp106-170.html

Weak well-posedness for a class of degenerate Lévy-driven SDEs with Hölder continuous coefficients

Author

Listed:
  • Marino, L.
  • Menozzi, S.

Abstract

In this article, we study the effects of the propagation of a non-degenerate Lévy noise through a chain of deterministic differential equations whose coefficients are Hölder continuous and satisfy a weak Hörmander-like condition. In particular, we assume some non-degeneracy with respect to the components which transmit the noise. Moreover, we characterize, for some specific dynamics, through suitable counter-examples, the almost sharp regularity exponents that ensure the weak well-posedness for the associated SDE. As a by-product of our approach, we also derive some Krylov-type estimates for the density of the weak solutions of the considered SDE.

Suggested Citation

  • Marino, L. & Menozzi, S., 2023. "Weak well-posedness for a class of degenerate Lévy-driven SDEs with Hölder continuous coefficients," Stochastic Processes and their Applications, Elsevier, vol. 162(C), pages 106-170.
    • Handle: RePEc:eee:spapps:v:162:y:2023:i:c:p:106-170
    DOI: 10.1016/j.spa.2023.04.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414923000807
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2023.04.012?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Paweł Sztonyk, 2010. "Estimates of Tempered Stable Densities," Journal of Theoretical Probability, Springer, vol. 23(1), pages 127-147, March.
    2. Menozzi, Stéphane, 2018. "Martingale problems for some degenerate Kolmogorov equations," Stochastic Processes and their Applications, Elsevier, vol. 128(3), pages 756-802.
    3. Krylov, N. V., 2004. "On weak uniqueness for some diffusions with discontinuous coefficients," Stochastic Processes and their Applications, Elsevier, vol. 113(1), pages 37-64, September.
    4. Li, Dingshi & Fan, Xiaoming, 2017. "Exponential stability of impulsive stochastic partial differential equations with delays," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 185-192.
    5. Ole E. Barndorff‐Nielsen & Neil Shephard, 2001. "Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
    6. Panki Kim & Renming Song, 2008. "Boundary Behavior of Harmonic Functions for Truncated Stable Processes," Journal of Theoretical Probability, Springer, vol. 21(2), pages 287-321, June.
    7. Cass, Thomas, 2009. "Smooth densities for solutions to stochastic differential equations with jumps," Stochastic Processes and their Applications, Elsevier, vol. 119(5), pages 1416-1435, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lucertini, Giacomo & Menozzi, Stéphane & Pagliarani, Stefano, 2025. "Strong regularization by noise for a class of kinetic SDEs driven by symmetric α-stable processes," Stochastic Processes and their Applications, Elsevier, vol. 189(C).

    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. Madan, Dilip B. & Wang, King, 2021. "The structure of financial returns," Finance Research Letters, Elsevier, vol. 40(C).
    2. Taufer, Emanuele & Leonenko, Nikolai, 2009. "Simulation of Lvy-driven Ornstein-Uhlenbeck processes with given marginal distribution," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2427-2437, April.
    3. Torben G. Andersen & Tim Bollerslev & Peter Christoffersen & Francis X. Diebold, 2007. "Practical Volatility and Correlation Modeling for Financial Market Risk Management," NBER Chapters, in: The Risks of Financial Institutions, pages 513-544, National Bureau of Economic Research, Inc.
    4. Álvaro Cartea & Thilo Meyer-Brandis, 2010. "How Duration Between Trades of Underlying Securities Affects Option Prices," Review of Finance, European Finance Association, vol. 14(4), pages 749-785.
    5. Julien Chevallier & Benoît Sévi, 2014. "On the Stochastic Properties of Carbon Futures Prices," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 58(1), pages 127-153, May.
    6. Jondeau, Eric, 2016. "Asymmetry in tail dependence in equity portfolios," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 351-368.
    7. Lars Stentoft, 2008. "American Option Pricing Using GARCH Models and the Normal Inverse Gaussian Distribution," Journal of Financial Econometrics, Oxford University Press, vol. 6(4), pages 540-582, Fall.
    8. A. Aghamohammadi & S. Mohammadi, 2017. "Bayesian analysis of penalized quantile regression for longitudinal data," Statistical Papers, Springer, vol. 58(4), pages 1035-1053, December.
    9. Robert Brooks & Robert Faff & Sirimon Treepongkaruna & Eliza Wu, 2015. "Do Sovereign Re-Ratings Destabilize Equity Markets during Financial Crises? New Evidence from Higher Return Moments," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 42(5-6), pages 777-799, June.
    10. Piotr Szczepocki, 2020. "Application of iterated filtering to stochastic volatility models based on non-Gaussian Ornstein-Uhlenbeck process," Statistics in Transition New Series, Polish Statistical Association, vol. 21(2), pages 173-187, June.
    11. Yan-Feng Wu & Xiangyu Yang & Jian-Qiang Hu, 2024. "Method of Moments Estimation for Affine Stochastic Volatility Models," Papers 2408.09185, arXiv.org.
    12. Caravenna, Francesco & Corbetta, Jacopo, 2018. "The asymptotic smile of a multiscaling stochastic volatility model," Stochastic Processes and their Applications, Elsevier, vol. 128(3), pages 1034-1071.
    13. Shinichiro Shirota & Yashiro Omori & Hedibert Lopes & Haixiang Piao, 2016. "Cholesky Realized Stochasti Volatility Model," Business and Economics Working Papers 224, Unidade de Negocios e Economia, Insper.
    14. Shibin Zhang & Xinsheng Zhang, 2013. "A least squares estimator for discretely observed Ornstein–Uhlenbeck processes driven by symmetric α-stable motions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(1), pages 89-103, February.
    15. Santos, Douglas G. & Candido, Osvaldo & Tófoli, Paula V., 2022. "Forecasting risk measures using intraday and overnight information," The North American Journal of Economics and Finance, Elsevier, vol. 60(C).
    16. Choi, Kyongwook & Yu, Wei-Choun & Zivot, Eric, 2010. "Long memory versus structural breaks in modeling and forecasting realized volatility," Journal of International Money and Finance, Elsevier, vol. 29(5), pages 857-875, September.
    17. Siddhartha Chib & Yasuhiro Omori & Manabu Asai, 2009. "Multivariate Stochastic Volatility," Springer Books, in: Thomas Mikosch & Jens-Peter Kreiß & Richard A. Davis & Torben Gustav Andersen (ed.), Handbook of Financial Time Series, chapter 16, pages 365-400, Springer.
    18. Schnurr Alexander & Woerner Jeannette H. C., 2011. "Well-balanced Lévy driven Ornstein–Uhlenbeck processes," Statistics & Risk Modeling, De Gruyter, vol. 28(4), pages 343-357, December.
    19. Todorov, Viktor & Tauchen, George & Grynkiv, Iaryna, 2014. "Volatility activity: Specification and estimation," Journal of Econometrics, Elsevier, vol. 178(P1), pages 180-193.
    20. Chiara Amorino & Arnaud Gloter, 2020. "Contrast function estimation for the drift parameter of ergodic jump diffusion process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(2), pages 279-346, June.

    More about this item

    Keywords

    ;
    ;
    ;

    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:162:y:2023:i:c:p:106-170. 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.