Systems of interacting diffusions with partial annihilation through membranes

Zhen Qing Chen; Wai Tong Fan

doi:10.1214/15-AOP1047

Systems of interacting diffusions with partial annihilation through membranes

Zhen Qing Chen, Wai Tong Fan

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

We introduce an interacting particle system in which two families of reflected diffusions interact in a singular manner near a deterministic interface I . This system can be used to model the transport of positive and negative charges in a solar cell or the population dynamics of two segregated species under competition. A related interacting random walk model with discrete state spaces has recently been introduced and studied in Chen and Fan (2014). In this paper, we establish the functional law of large numbers for this new system, thereby extending the hydrodynamic limit in Chen and Fan (2014) to reflected diffusions in domains with mixed-type boundary conditions, which include absorption (harvest of electric charges). We employ a new and direct approach that avoids going through the delicate BBGKY hierarchy.

Original language	English
Pages (from-to)	100-146
Number of pages	47
Journal	Annals of Probability
Volume	45
Issue number	1
DOIs	https://doi.org/10.1214/15-AOP1047
Publication status	Published - 2017
Externally published	Yes

Keywords

Annihilation
Coupled partial differential equation
Dirichlet form
Hydrodynamic limit
Interacting diffusion
Martingales
Nonlinear boundary condition
Reflected diffusion

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10.1214/15-AOP1047

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Chen, Z. Q., & Fan, W. T. (2017). Systems of interacting diffusions with partial annihilation through membranes. Annals of Probability, 45(1), 100-146. https://doi.org/10.1214/15-AOP1047

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AU - Fan, Wai Tong

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N2 - We introduce an interacting particle system in which two families of reflected diffusions interact in a singular manner near a deterministic interface I . This system can be used to model the transport of positive and negative charges in a solar cell or the population dynamics of two segregated species under competition. A related interacting random walk model with discrete state spaces has recently been introduced and studied in Chen and Fan (2014). In this paper, we establish the functional law of large numbers for this new system, thereby extending the hydrodynamic limit in Chen and Fan (2014) to reflected diffusions in domains with mixed-type boundary conditions, which include absorption (harvest of electric charges). We employ a new and direct approach that avoids going through the delicate BBGKY hierarchy.

AB - We introduce an interacting particle system in which two families of reflected diffusions interact in a singular manner near a deterministic interface I . This system can be used to model the transport of positive and negative charges in a solar cell or the population dynamics of two segregated species under competition. A related interacting random walk model with discrete state spaces has recently been introduced and studied in Chen and Fan (2014). In this paper, we establish the functional law of large numbers for this new system, thereby extending the hydrodynamic limit in Chen and Fan (2014) to reflected diffusions in domains with mixed-type boundary conditions, which include absorption (harvest of electric charges). We employ a new and direct approach that avoids going through the delicate BBGKY hierarchy.

KW - Annihilation

KW - Coupled partial differential equation

KW - Dirichlet form

KW - Hydrodynamic limit

KW - Interacting diffusion

KW - Martingales

KW - Nonlinear boundary condition

KW - Reflected diffusion

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DO - 10.1214/15-AOP1047

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JO - Annals of Probability

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Systems of interacting diffusions with partial annihilation through membranes

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Keywords

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