9 papers
Multilevel Monte Carlo learning
Thomas Gerstner, Bastian Harrach, Daniel Roth +1
In this work, we study the approximation of expected values of functional quantities on the solution of a stochastic differential equation (SDE), where we replace the Monte Carlo e…
Convergence of Milstein Brownian bridge Monte Carlo methods and stable Greeks calculation
Thomas Gerstner, Bastian Harrach, Daniel Roth
We consider the pricing and the sensitivity calculation of continuously monitored barrier options. Standard Monte Carlo algorithms work well for pricing these options. Therefore th…
Monotonicity-based inversion of the fractional Schrödinger equation II. General potentials and stability
Bastian Harrach, Yi-Hsuan Lin
In this work, we use monotonicity-based methods for the fractional Schrödinger equation with general potentials in a Lipschitz bounded open set $Ω\subset \mathbb…
Dimension bounds in monotonicity methods for the Helmholtz equation
Bastian Harrach, Valter Pohjola, Mikko Salo
The article [HPS] established a monotonicity inequality for the Helmholtz equation and presented applications to shape detection and local uniqueness in inverse boundary problems.…
Beyond the Bakushinskii veto: Regularising linear inverse problems without knowing the noise distribution
Bastian Harrach, Tim Jahn, Roland Potthast
This article deals with the solution of linear ill-posed equations in Hilbert spaces. Often, one only has a corrupted measurement of the right hand side at hand and the Bakushinski…
Local uniqueness for an inverse boundary value problem with partial data
Bastian Harrach, Marcel Ullrich
In dimension , we prove a local uniqueness result for the potentials of the Schrödinger equation from partial boundary data. More precisely, we show that po…