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Annihilating branching processes

Publication ,  Journal Article
Bramson, M; Wan-ding, D; Durrett, R
Published in: Stochastic Processes and their Applications
January 1, 1991

We consider Markov processes ηt ⊂ Zd in which (i) particles die at rate δ ≥ 0, (ii) births from x to a neighboring y occur at rate 1, and (iii) when a new particle lands on an occupied site the particles annihilate each other and a vacant site results. When δ = 0 product measure with density 1 2 is a stationary distribution; we show it is the limit whenever P(η0≠ ø) = 1. We also show that if δ is small there is a nontrivial stationary distribution, and that for any δ there are most two extremal translation invariant stationary distributions. © 1991.

Duke Scholars

Published In

Stochastic Processes and their Applications

DOI

ISSN

0304-4149

Publication Date

January 1, 1991

Volume

37

Issue

1

Start / End Page

1 / 17

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 4901 Applied mathematics
  • 1502 Banking, Finance and Investment
  • 0104 Statistics
  • 0102 Applied Mathematics
 

Citation

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ICMJE
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Bramson, M., Wan-ding, D., & Durrett, R. (1991). Annihilating branching processes. Stochastic Processes and Their Applications, 37(1), 1–17. https://doi.org/10.1016/0304-4149(91)90056-I
Bramson, M., D. Wan-ding, and R. Durrett. “Annihilating branching processes.” Stochastic Processes and Their Applications 37, no. 1 (January 1, 1991): 1–17. https://doi.org/10.1016/0304-4149(91)90056-I.
Bramson M, Wan-ding D, Durrett R. Annihilating branching processes. Stochastic Processes and their Applications. 1991 Jan 1;37(1):1–17.
Bramson, M., et al. “Annihilating branching processes.” Stochastic Processes and Their Applications, vol. 37, no. 1, Jan. 1991, pp. 1–17. Scopus, doi:10.1016/0304-4149(91)90056-I.
Bramson M, Wan-ding D, Durrett R. Annihilating branching processes. Stochastic Processes and their Applications. 1991 Jan 1;37(1):1–17.
Journal cover image

Published In

Stochastic Processes and their Applications

DOI

ISSN

0304-4149

Publication Date

January 1, 1991

Volume

37

Issue

1

Start / End Page

1 / 17

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 4901 Applied mathematics
  • 1502 Banking, Finance and Investment
  • 0104 Statistics
  • 0102 Applied Mathematics