Discrete approximations to local times for reflected diffusions
نویسنده
چکیده
For an arbitrary bounded Lipschitz domain D, we propose a class of discrete analogues for the boundary local time of reflected diffusions in D. These discrete analogues are obtained from random walks on D := D ∩ 2−kZd and can be effectively simulated in practice. We prove weak convergence of the joint law of the random walks and the proposed analogues to the joint law of reflected diffusion and its boundary local time. A cornerstone in the proof is the local limit theorem for reflected diffusions. AMS 2010 subject classifications: Primary 60F17, 60J55; Secondary 35K10, 35J25, 49M25.
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