Open Access
2016 Discrete approximations to local times for reflected diffusions
Wai-Tong Louis Fan
Electron. Commun. Probab. 21: 1-12 (2016). DOI: 10.1214/16-ECP4694


We propose a discrete analogue for the boundary local time of reflected diffusions in bounded Lipschitz domains. This discrete analogue, called the discrete local time, can be effectively simulated in practice and is obtained pathwise from random walks on lattices. We establish weak convergence of the joint law of the discrete local time and the associated random walks as the lattice size decreases to zero. A cornerstone of the proof is the local central limit theorem for reflected diffusions developed in [7]. Applications of the join convergence result to PDE problems are illustrated.


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Wai-Tong Louis Fan. "Discrete approximations to local times for reflected diffusions." Electron. Commun. Probab. 21 1 - 12, 2016.


Received: 10 November 2015; Accepted: 19 February 2016; Published: 2016
First available in Project Euclid: 23 February 2016

zbMATH: 1336.60068
MathSciNet: MR3485385
Digital Object Identifier: 10.1214/16-ECP4694

Primary: 60F17 , 60J55
Secondary: 35J25 , 35K10 , 49M25

Keywords: heat kernel , Local time , Random walk , Reflected diffusion , Robin boundary problem

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