# ε-Strong simulation of the Brownian path

@article{Beskos2011StrongSO, title={$\epsilon$-Strong simulation of the Brownian path}, author={Alexandros Beskos and Stefano Peluchetti and Gareth O. Roberts}, journal={Bernoulli}, year={2011}, volume={18}, pages={1223-1248} }

We present an iterative sampling method which delivers upper and lower bounding processes for the Brownian path. We develop such processes with particular emphasis on being able to unbiasedly simulate them on a personal computer. The dominating processes converge almost surely in the supremum and L 1 norms. In particular, the rate of converge in L 1 is of the order O(K −1/2 ) , K denoting the computing cost. The a.s. enfolding of the Brownian path can be exploited in Monte Carlo applications…

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