Johannes Brutsche

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math.ST2026

Sharp adaptive nonparametric testing for constant volatility

Johannes Brutsche, Lukas Riepl

Based on discrete observations, we develop a test to infer if the volatility function $I ¨ (\cdot)$ within the nonparametric Gaussian white noise model $d Y_{t} = I ¨ (t) d W_{t}$ is constant…

math.ST2026

Self-organized regime switching in null-recurrent dynamics

Johannes Brutsche, Sebastian Hahn, Angelika Rohde

Based on discrete observations $X_{0}, X_{I^} , \dots, X_{n I^}$ for $I^ = n^{- I^^{3}}$ with $I^^{3} \in [0, 1)$ of the null-recurrent dynamic $d X_{t} = I ¨ (X_{t}) d W_{t}$ with a Brownian motion $W$ and $Ï(x…

math.ST2026

The level of self-organized criticality in oscillating Brownian motion: $n$ -consistency and stable Poisson-type convergence of the MLE

Johannes Brutsche, Angelika Rohde

For some discretely observed path of oscillating Brownian motion with level of self-organized criticality $I ¨ _{0}$ , we prove in the infill asymptotics that the MLE is $n$ -consistent,…

math.ST2024

Sharp adaptive and pathwise stable similarity testing for scalar ergodic diffusions

Johannes Brutsche, Angelika Rohde

Within the nonparametric diffusion model, we develop a multiple test to infer about similarity of an unknown drift $b$ to some reference drift $b_{0}$ : At prescribed significance, we…

Sharp adaptive nonparametric testing for constant volatility

Self-organized regime switching in null-recurrent dynamics

The level of self-organized criticality in oscillating Brownian motion: n-consistency and stable Poisson-type convergence of the MLE

Sharp adaptive and pathwise stable similarity testing for scalar ergodic diffusions

The level of self-organized criticality in oscillating Brownian motion: $n$ -consistency and stable Poisson-type convergence of the MLE