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Mathematics > Probability

arXiv:1405.6469 (math)
[Submitted on 26 May 2014 (v1), last revised 30 Aug 2017 (this version, v3)]

Title:Exact Simulation of Multidimensional Reflected Brownian Motion

Authors:Jose Blanchet, Karthyek R. A. Murthy
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Abstract:We present the first exact simulation method for multidimensional reflected Brownian motion (RBM). Exact simulation in this setting is challenging because of the presence of correlated local-time-like terms in the definition of RBM. We apply recently developed so-called $\varepsilon-$strong simulation techniques (also known as Tolerance-Enforced Simulation) which allow us to provide a piece-wise linear approximation to RBM with $\varepsilon $ (deterministic) error in uniform norm. A novel conditional acceptance/rejection step is then used to eliminate the error. In particular, we condition on a suitably designed information structure so that a feasible proposal distribution can be applied.
Subjects: Probability (math.PR); Computation (stat.CO)
MSC classes: 65C05, 65C05 (Primary) 60J60, 60J65 (Secondary)
Cite as: arXiv:1405.6469 [math.PR]
  (or arXiv:1405.6469v3 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.1405.6469

Submission history

From: Karthyek Rajhaa Annaswamy Murthy [view email]
[v1] Mon, 26 May 2014 06:17:36 UTC (20 KB)
[v2] Sat, 27 Sep 2014 06:04:41 UTC (20 KB)
[v3] Wed, 30 Aug 2017 16:12:33 UTC (29 KB)
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