Large Deviations for Brownian Particle Systems with Killing

Amarjit Budhiraja (), Wai-Tong (Louis) Fan () and Ruoyu Wu ()
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Amarjit Budhiraja: University of North Carolina
Wai-Tong (Louis) Fan: University of Wisconsin
Ruoyu Wu: Brown University

Journal of Theoretical Probability, 2018, vol. 31, issue 3, 1779-1818

Abstract: 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; 60F10; 60K35; 60B10; 93E20 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10959-017-0764-2

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