Exact simulation of multidimensional reflected Brownian motion

• DOI: 10.1017/jpr.2018.10
• Publication Date: 2018-03-28T04:20:44Z
• Authors: Jose Blanchet; Karthyek Murthy
• Keywords: FOS: Computer and information sciences; Probability (math.PR); FOS: Mathematics; 0101 mathematics; Statistics - Computation; 01 natural sciences; Mathematics - Probability; Computation (stat.CO); 65C05, 65C05 (Primary) 60J60, 60J65 (Secondary)

Abstract We present the first exact simulation method for multidimensional reflected Brownian motion (RBM). Exact in this setting is challenging because of presence correlated local-time-like terms definition RBM. apply recently developed so-called ε-strong techniques (also known as tolerance-enforced simulation) which allow us to provide a piecewise linear approximation RBM with ε (deterministic) error uniform norm. A novel conditional acceptance–rejection step then used eliminate error. In particular, we condition on suitably designed information structure so that feasible proposal distribution can be applied.