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Large Deviations for Brownian Particle Systems with Killing

  • Amarjit Budhiraja
  • Wai-Tong (Louis) Fan
  • Ruoyu Wu
Article

Abstract

Particle approximations for certain nonlinear and nonlocal reaction–diffusion equations are studied using a system of Brownian motions with killing. The system is described by a collection of i.i.d. Brownian particles where each particle is killed independently at a rate determined by the empirical sub-probability measure of the states of the particles alive. A large deviation principle (LDP) for such sub-probability measure-valued processes is established. Along the way a convenient variational representation, which is of independent interest, for expectations of nonnegative functionals of Brownian motions together with an i.i.d. sequence of random variables is established. Proof of the LDP relies on this variational representation and weak convergence arguments.

Keywords

Large deviations Weakly interacting particle systems Brownian particles with killing Nonlinear reaction–diffusion equations Variational representations 

Mathematics Subject Classification (2010)

60F10 60K35 60B10 93E20 

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of Statistics and Operations ResearchUniversity of North CarolinaChapel HillUSA
  2. 2.Department of MathematicsUniversity of WisconsinMadisonUSA
  3. 3.Division of Applied MathematicsBrown UniversityProvidenceUSA

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