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math.PR2016★ 7 cited
Weak convergence rates for numerical approximations of stochastic partial differential equations with nonlinear diffusion coefficients in UMD Banach spaces
Mario Hefter, Arnulf Jentzen, Ryan Kurniawan
Strong convergence rates for numerical approximations of semilinear stochastic partial differential equations (SPDEs) with smooth and regular nonlinearities are well understood in…
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…