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Discretization error in simulation of one-dimensional reflecting Brownian motion. (English) Zbl 0853.65147
It is shown that the discretization error associated with the Euler scheme for simulation of one-dimensional reflected Brownian motion has both a strong and weak order of convergence of precisely 1/2. The asymptotic distribution of the discretization error is also described. Finally, a number of improved approximations to the simulation of reflected Brownian motion are provided.

MSC:
65C99 Probabilistic methods, stochastic differential equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60J65 Brownian motion
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