Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 21 (2016), paper no. 16, 12 pp.
Discrete approximations to local times for reflected diffusions
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 . Applications of the join convergence result to PDE problems are illustrated.
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
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
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
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