IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v21y2019i3d10.1007_s11009-017-9581-4.html
   My bibliography  Save this article

Symmetry in the Green’s Function for Birth-death Chains

Author

Listed:
  • Greg Markowsky

    (Monash University)

  • José Luis Palacios

    (The University of New Mexico)

Abstract

A symmetric relation in the probabilistic Green’s function for birth-death chains is explored. Two proofs are given, each of which makes use of the known symmetry of the Green’s functions in other contexts. The first uses as primary tool the local time of Brownian motion, while the second uses the reciprocity principle from electric network theory. We also show that the the second proof extends easily to cover birth-death chains (a.k.a. state-dependent random walks) on trees, and can be adapted in order to derive hitting times on trees.

Suggested Citation

  • Greg Markowsky & José Luis Palacios, 2019. "Symmetry in the Green’s Function for Birth-death Chains," Methodology and Computing in Applied Probability, Springer, vol. 21(3), pages 841-851, September.
    • Handle: RePEc:spr:metcap:v:21:y:2019:i:3:d:10.1007_s11009-017-9581-4
    DOI: 10.1007/s11009-017-9581-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-017-9581-4
    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/s11009-017-9581-4?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. Markowsky, Greg, 2011. "Applying Brownian motion to the study of birth-death chains," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1173-1178, August.
    2. Palacios, JoséLuis & Tetali, Prasad, 1996. "A note on expected hitting times for birth and death chains," Statistics & Probability Letters, Elsevier, vol. 30(2), pages 119-125, October.
    3. José Luis Palacios & Daniel Quiroz, 2016. "Birth and Death Chains on Finite Trees: Computing their Stationary Distribution and Hitting Times," Methodology and Computing in Applied Probability, Springer, vol. 18(2), pages 487-498, June.
    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. Bapat, R.B., 2011. "On the first passage time of a simple random walk on a tree," Statistics & Probability Letters, Elsevier, vol. 81(10), pages 1552-1558, October.
    2. Palacios, José Luis, 2000. "A note on circular Markov chains," Statistics & Probability Letters, Elsevier, vol. 47(3), pages 301-306, April.
    3. José Luis Palacios & Daniel Quiroz, 2016. "Birth and Death Chains on Finite Trees: Computing their Stationary Distribution and Hitting Times," Methodology and Computing in Applied Probability, Springer, vol. 18(2), pages 487-498, June.
    4. Haiyan, Chen & Fuji, Zhang, 2004. "The expected hitting times for graphs with cutpoints," Statistics & Probability Letters, Elsevier, vol. 66(1), pages 9-17, January.
    5. Wang, Chengyong & Guo, Ziliang & Li, Shuchao, 2018. "Expected hitting times for random walks on the k-triangle graph and their applications," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 698-710.

    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:metcap:v:21:y:2019:i:3:d:10.1007_s11009-017-9581-4. 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.