5 papers
Adaptive Quantile Computation for Brownian Bridge in Change-Point Analysis
Jürgen Franke, Mario Hefter, André Herzwurm +2
As an example for the fast calculation of distributional parameters of Gaussian processes, we propose a new Monte Carlo algorithm for the computation of quantiles of the supremum n…
Lower Error Bounds for Strong Approximation of Scalar SDEs with non-Lipschitzian Coefficients
Mario Hefter, André Herzwurm, Thomas Müller-Gronbach
We study pathwise approximation of scalar stochastic differential equations at a single time point or globally in time by means of methods that are based on finitely many observati…
Strong Convergence Rates for Cox-Ingersoll-Ross Processes - Full Parameter Range
Mario Hefter, André Herzwurm
We study strong (pathwise) approximation of Cox-Ingersoll-Ross processes. We propose a Milstein-type scheme that is suitably truncated close to zero, where the diffusion coefficien…
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…
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…