IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v336y2018icp36-46.html
   My bibliography  Save this article

Stochastic fractional evolution equations with fractional brownian motion and infinite delay

Author

Listed:
  • Xu, Liping
  • Li, Zhi

Abstract

In this paper, we consider a class of stochastic fractional evolution equations with infinite delay and a fractional Brownian motion in a Hilbert space. By the stochastic analysis technique, we establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz condition with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory.

Suggested Citation

  • Xu, Liping & Li, Zhi, 2018. "Stochastic fractional evolution equations with fractional brownian motion and infinite delay," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 36-46.
    • Handle: RePEc:eee:apmaco:v:336:y:2018:i:c:p:36-46
    DOI: 10.1016/j.amc.2018.04.060
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300318303862
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2018.04.060?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. Boufoussi, Brahim & Hajji, Salah, 2012. "Neutral stochastic functional differential equations driven by a fractional Brownian motion in a Hilbert space," Statistics & Probability Letters, Elsevier, vol. 82(8), pages 1549-1558.
    2. Simonsen, Ingve, 2003. "Measuring anti-correlations in the nordic electricity spot market by wavelets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 322(C), pages 597-606.
    3. Fabienne Comte & Eric Renault, 1998. "Long memory in continuous‐time stochastic volatility models," Mathematical Finance, Wiley Blackwell, vol. 8(4), pages 291-323, October.
    4. Ingve Simonsen, 2001. "Measuring Anti-Correlations in the Nordic Electricity Spot Market by Wavelets," Papers cond-mat/0108033, arXiv.org, revised Apr 2003.
    5. Luo, Jiaowan & Liu, Kai, 2008. "Stability of infinite dimensional stochastic evolution equations with memory and Markovian jumps," Stochastic Processes and their Applications, Elsevier, vol. 118(5), pages 864-895, May.
    6. Comte, F. & Renault, E., 1996. "Long memory continuous time models," Journal of Econometrics, Elsevier, vol. 73(1), pages 101-149, July.
    7. Röckner, Michael & Zhu, Rongchan & Zhu, Xiangchan, 2014. "Local existence and non-explosion of solutions for stochastic fractional partial differential equations driven by multiplicative noise," Stochastic Processes and their Applications, Elsevier, vol. 124(5), pages 1974-2002.
    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. Li, Zhi & Yan, Litan, 2018. "Harnack inequalities for SDEs driven by subordinator fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 134(C), pages 45-53.
    2. Lavička, Hynek & Kracík, Jiří, 2020. "Fluctuation analysis of electric power loads in Europe: Correlation multifractality vs. Distribution function multifractality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    3. Mikkel Bennedsen & Asger Lunde & Mikko S. Pakkanen, 2017. "Decoupling the short- and long-term behavior of stochastic volatility," CREATES Research Papers 2017-26, Department of Economics and Business Economics, Aarhus University.
    4. Michel Culot & Valérie Goffin & Steve Lawford & Sébastien de Meten & Yves Smeers, 2013. "Practical stochastic modelling of electricity prices," Post-Print hal-01021603, HAL.
    5. Vanessa Didelez, 2008. "Graphical models for marked point processes based on local independence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 245-264, February.
    6. Juraj Čurpek, 2019. "Time Evolution of Hurst Exponent: Czech Wholesale Electricity Market Study," European Financial and Accounting Journal, Prague University of Economics and Business, vol. 2019(3), pages 25-44.
    7. Kanaya, Shin & Kristensen, Dennis, 2016. "Estimation Of Stochastic Volatility Models By Nonparametric Filtering," Econometric Theory, Cambridge University Press, vol. 32(4), pages 861-916, August.
    8. Manabu Asai & Michael McAleer, 2017. "A fractionally integrated Wishart stochastic volatility model," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 42-59, March.
    9. Ignatieva Katja, 2014. "A nonparametric model for spot price dynamics and pricing of futures contracts in electricity markets," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 18(5), pages 483-505, December.
    10. Marina Resta & Davide Sciutti, 2003. "Spot price dynamics in deregulated power markets," Econometrics 0312002, University Library of Munich, Germany.
    11. Blanka Horvath & Antoine Jacquier & Aitor Muguruza & Andreas Sojmark, 2017. "Functional central limit theorems for rough volatility," Papers 1711.03078, arXiv.org, revised Nov 2023.
    12. Fan, Qingju & Li, Dan, 2015. "Multifractal cross-correlation analysis in electricity spot market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 429(C), pages 17-27.
    13. Chen, Xiaohong & Hansen, Lars Peter & Carrasco, Marine, 2010. "Nonlinearity and temporal dependence," Journal of Econometrics, Elsevier, vol. 155(2), pages 155-169, April.
    14. Nielsen, Morten Ørregaard & Frederiksen, Per, 2008. "Finite sample accuracy and choice of sampling frequency in integrated volatility estimation," Journal of Empirical Finance, Elsevier, vol. 15(2), pages 265-286, March.
    15. Inoua, Sabiou M. & Smith, Vernon L., 2023. "A classical model of speculative asset price dynamics," Journal of Behavioral and Experimental Finance, Elsevier, vol. 37(C).
    16. Antoine Jacquier & Claude Martini & Aitor Muguruza, 2018. "On VIX futures in the rough Bergomi model," Quantitative Finance, Taylor & Francis Journals, vol. 18(1), pages 45-61, January.
    17. Suchetana Sadhukhan & Poulomi Sadhukhan, 2022. "Sector-wise analysis of Indian stock market: Long and short-term risk and stability analysis," Papers 2210.09619, arXiv.org.
    18. Casas, Isabel & Gao, Jiti, 2008. "Econometric estimation in long-range dependent volatility models: Theory and practice," Journal of Econometrics, Elsevier, vol. 147(1), pages 72-83, November.
    19. Eduardo Rossi & Paolo Santucci de Magistris, 2014. "Estimation of Long Memory in Integrated Variance," Econometric Reviews, Taylor & Francis Journals, vol. 33(7), pages 785-814, October.
    20. Mikkel Bennedsen, 2016. "Semiparametric inference on the fractal index of Gaussian and conditionally Gaussian time series data," CREATES Research Papers 2016-21, Department of Economics and Business Economics, Aarhus University.

    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:apmaco:v:336:y:2018:i:c:p:36-46. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.