IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v414y2014icp154-162.html
   My bibliography  Save this article

Itô formula for one-dimensional continuous-time quantum random walk

Author

Listed:
  • Kang, Yuanbao
  • Wang, Caishi

Abstract

In the paper, we first extend the discrete time quantum random walk (DQRW) to continuous time quantum random walk (CQRW). Then we establish an Itô formula for the one-dimensional CQRW. As an application, we present Tanaka’s formula with the Itô formula and characterize the relation between quantum local time Lta and Dirac delta function δ. Finally, we discuss quantum stochastic calculus for the CQRW.

Suggested Citation

  • Kang, Yuanbao & Wang, Caishi, 2014. "Itô formula for one-dimensional continuous-time quantum random walk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 414(C), pages 154-162.
    • Handle: RePEc:eee:phsmap:v:414:y:2014:i:c:p:154-162
    DOI: 10.1016/j.physa.2014.06.086
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437114005743
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2014.06.086?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. Biane, Philippe, 2010. "Itô's stochastic calculus and Heisenberg commutation relations," Stochastic Processes and their Applications, Elsevier, vol. 120(5), pages 698-720, May.
    2. Kunita, Hiroshi, 2010. "Itô's stochastic calculus: Its surprising power for applications," Stochastic Processes and their Applications, Elsevier, vol. 120(5), pages 622-652, May.
    3. Da Pelo, Paolo & Lanconelli, Alberto & Stan, Aurel I., 2013. "An Itô formula for a family of stochastic integrals and related Wong–Zakai theorems," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 3183-3200.
    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. Kang, Yuanbao, 2016. "Quantum decomposition of random walk on Cayley graph of finite group," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 458(C), pages 146-156.

    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. Yu, Jingyi & Liu, Meng, 2017. "Stationary distribution and ergodicity of a stochastic food-chain model with Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 14-28.
    2. Liu, Meng & Bai, Chuanzhi, 2016. "Dynamics of a stochastic one-prey two-predator model with Lévy jumps," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 308-321.
    3. Lanconelli, Alberto & Scorolli, Ramiro, 2021. "Wong–Zakai approximations for quasilinear systems of Itô’s type stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 141(C), pages 57-78.
    4. Oscar García, 2019. "Estimating reducible stochastic differential equations by conversion to a least-squares problem," Computational Statistics, Springer, vol. 34(1), pages 23-46, March.
    5. Biane, Philippe, 2010. "Itô's stochastic calculus and Heisenberg commutation relations," Stochastic Processes and their Applications, Elsevier, vol. 120(5), pages 698-720, May.
    6. Zhao, Yu & Yuan, Sanling, 2017. "Optimal harvesting policy of a stochastic two-species competitive model with Lévy noise in a polluted environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 477(C), pages 20-33.
    7. Bilel Kacem Ben Ammou & Alberto Lanconelli, 2019. "Rate of Convergence for Wong–Zakai-Type Approximations of Itô Stochastic Differential Equations," Journal of Theoretical Probability, Springer, vol. 32(4), pages 1780-1803, December.
    8. Gao, Miaomiao & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2019. "Threshold behavior of a stochastic Lotka–Volterra food chain chemostat model with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 191-203.
    9. Ishikawa, Yasushi & Kunita, Hiroshi & Tsuchiya, Masaaki, 2018. "Smooth density and its short time estimate for jump process determined by SDE," Stochastic Processes and their Applications, Elsevier, vol. 128(9), pages 3181-3219.
    10. Zhang, Xinhong & Li, Wenxue & Liu, Meng & Wang, Ke, 2015. "Dynamics of a stochastic Holling II one-predator two-prey system with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 571-582.
    11. Lanconelli, Alberto, 2018. "Standardizing densities on Gaussian spaces," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 243-250.
    12. Gao, Miaomiao & Jiang, Daqing, 2019. "Analysis of stochastic multimolecular biochemical reaction model with lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 601-613.
    13. Zura Kakushadze, 2016. "On Origins of Bubbles," Papers 1610.03769, arXiv.org, revised Jul 2017.
    14. Wang, Hui & Pan, Fangmei & Liu, Meng, 2019. "Survival analysis of a stochastic service–resource mutualism model in a polluted environment with pulse toxicant input," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 591-606.
    15. Tan, Li & Jin, Wei & Hou, Zhenting, 2013. "Weak convergence of functional stochastic differential equations with variable delays," Statistics & Probability Letters, Elsevier, vol. 83(11), pages 2592-2599.
    16. Okhrati, Ramin & Balbás, Alejandro & Garrido, José, 2014. "Hedging of defaultable claims in a structural model using a locally risk-minimizing approach," Stochastic Processes and their Applications, Elsevier, vol. 124(9), pages 2868-2891.
    17. Jorge Sanchez-Ortiz & Omar U. Lopez-Cresencio & Francisco J. Ariza-Hernandez & Martin P. Arciga-Alejandre, 2021. "Cauchy Problem for a Stochastic Fractional Differential Equation with Caputo-Itô Derivative," Mathematics, MDPI, vol. 9(13), pages 1-10, June.
    18. Liu, Meng & Bai, Chuanzhi, 2016. "Optimal harvesting of a stochastic mutualism model with Lévy jumps," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 301-309.
    19. Liu, Meng & Deng, Meiling & Du, Bo, 2015. "Analysis of a stochastic logistic model with diffusion," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 169-182.
    20. Xiaoling Zou & Ke Wang, 2014. "Optimal Harvesting for a Logistic Population Dynamics Driven by a Lévy Process," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 969-979, June.

    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:phsmap:v:414:y:2014:i:c:p:154-162. 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.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.