TY - CHAP

T1 - Some path large-deviation results for a branching diffusion

AU - Hardy, R

AU - Harris, S C

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

UR - http://dx.doi.org/10.1007/978-1-4614-6240-8_5

U2 - 10.1007/978-1-4614-6240-8_5

DO - 10.1007/978-1-4614-6240-8_5

M3 - Chapter

SN - 9781461462392

T3 - Springer Proceedings in Mathematics & Statistics

SP - 61

EP - 91

BT - Advances in Superprocesses and Nonlinear PDEs

A2 - Englander, Janos

A2 - Rider, Brian

PB - Springer

CY - New York

ER -