Electronic Communications in Probability

Discrete approximations to local times for reflected diffusions

Wai-Tong Louis Fan

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1456238572

Digital Object Identifier
doi:10.1214/16-ECP4694

Mathematical Reviews number (MathSciNet)
MR3485385

Zentralblatt MATH identifier
1336.60068

Subjects
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

Keywords
random walk reflected diffusion local time heat kernel Robin boundary problem

Rights
Creative Commons Attribution 4.0 International License.

Citation

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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References

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