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math.PR2016
Optimal Strong Approximation of the One-dimensional Squared {B}essel Process
Mario Hefter, André Herzwurm
We consider the one-dimensional squared Bessel process given by the stochastic differential equation (SDE) \begin{align*} dX_t = 1\,dt + 2\sqrt{X_t}\,dW_t, \quad X_0=x_0, \quad t\i…
math.PR2016
Adaptive Approximation of the Minimum of Brownian Motion
James M. Calvin, Mario Hefter, André Herzwurm
We study the error in approximating the minimum of a Brownian motion on the unit interval based on finitely many point evaluations. We construct an algorithm that adaptively choose…