Electronic Communications in Probability

Discrete approximations to local times for reflected diffusions

Wai-Tong Louis Fan

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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.

Article information

Electron. Commun. Probab. Volume 21 (2016), paper no. 16, 12 pp.

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

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Zentralblatt MATH identifier

Primary: 60F17: Functional limit theorems; invariance principles 60J55: Local time and additive functionals
Secondary: 35K10: Second-order parabolic equations 35J25: Boundary value problems for second-order elliptic equations 49M25: Discrete approximations

random walk reflected diffusion local time heat kernel Robin boundary problem

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Fan, Wai-Tong Louis. Discrete approximations to local times for reflected diffusions. Electron. Commun. Probab. 21 (2016), paper no. 16, 12 pp. doi:10.1214/16-ECP4694. https://projecteuclid.org/euclid.ecp/1456238572

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