Some path large-deviation results for a branching diffusion

R Hardy, S C Harris

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

We give an intuitive proof of a path large-deviations result for a typed branching diffusion as found in Git, J.Harris and S.C.Harris (Ann. App. Probab. 17(2):609-653, 2007). Our approach involves an application of a change of measure technique involving a distinguished infinite line of descent, or spine, and we follow the spine set-up of Hardy and Harris (Séminaire de Probabilités XLII:281-330, 2009). Our proof combines simple martingale ideas with applications of Varadhan's lemma and is successful mainly because a "spine decomposition" effectively reduces otherwise difficult calculations on the whole collection of branching diffusion particles down to just a single particle (the spine) whose large-deviations behaviour is well known. A similar approach was used for branching Brownian motion in Hardy and Harris (Stoch. Process. Appl. 116(12):1992-2013, 2006). Importantly, our techniques should be applicable in a much wider class of branching diffusion large-deviations problems.
Original languageEnglish
Title of host publicationAdvances in Superprocesses and Nonlinear PDEs
EditorsJanos Englander, Brian Rider
Place of PublicationNew York
PublisherSpringer
Pages61-91
ISBN (Electronic)9781461462408
ISBN (Print)9781461462392
DOIs
Publication statusPublished - 2013

Publication series

NameSpringer Proceedings in Mathematics & Statistics
PublisherSpringer
Volume38
ISSN (Print)2194-1009

Fingerprint

Spine
Large Deviations
Branching
Path
Branching Brownian Motion
Change of Measure
Descent
Martingale
Intuitive
Lemma
Decompose
Line

Cite this

Hardy, R., & Harris, S. C. (2013). Some path large-deviation results for a branching diffusion. In J. Englander, & B. Rider (Eds.), Advances in Superprocesses and Nonlinear PDEs (pp. 61-91). (Springer Proceedings in Mathematics & Statistics; Vol. 38). New York: Springer. https://doi.org/10.1007/978-1-4614-6240-8_5

Some path large-deviation results for a branching diffusion. / Hardy, R; Harris, S C.

Advances in Superprocesses and Nonlinear PDEs. ed. / Janos Englander; Brian Rider. New York : Springer, 2013. p. 61-91 (Springer Proceedings in Mathematics & Statistics; Vol. 38).

Research output: Chapter in Book/Report/Conference proceedingChapter

Hardy, R & Harris, SC 2013, Some path large-deviation results for a branching diffusion. in J Englander & B Rider (eds), Advances in Superprocesses and Nonlinear PDEs. Springer Proceedings in Mathematics & Statistics, vol. 38, Springer, New York, pp. 61-91. https://doi.org/10.1007/978-1-4614-6240-8_5
Hardy R, Harris SC. Some path large-deviation results for a branching diffusion. In Englander J, Rider B, editors, Advances in Superprocesses and Nonlinear PDEs. New York: Springer. 2013. p. 61-91. (Springer Proceedings in Mathematics & Statistics). https://doi.org/10.1007/978-1-4614-6240-8_5
Hardy, R ; Harris, S C. / Some path large-deviation results for a branching diffusion. Advances in Superprocesses and Nonlinear PDEs. editor / Janos Englander ; Brian Rider. New York : Springer, 2013. pp. 61-91 (Springer Proceedings in Mathematics & Statistics).
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