Selected Publications
- Philipp Harms, David Stefanovits. Affine representations of fractional processes with applications in mathematical finance. Accepted for publication in Stochastic Processes and their Applications (2018). arXiv:1510.04061
- Philipp Harms, David Stefanovits, Josef Teichmann, Mario Wüthrich. Consistent recalibration of yield curve models. Mathematical Finance (2017), pp. 1-43. arXiv:1502.02926.
- Philipp Harms, Marvin Müller. Weak convergence rates for stochastic evolution equations and applications to nonlinear stochastic wave, HJMM, stochastic Schroedinger and linearized stochastic Korteweg-de Vries equations. arXiv:1710.01273.
- Martin Bauer, Martins Bruveris, Philipp Harms, Jakob Møller-Andersen. A numerical framework for Sobolev metrics on the space of curves. SIAM Journal on Imaging Sciences 10, 1 (2017), pp. 47-73. arXiv:1603.03480. Code available on https://github.com/h2metrics/h2metrics.
- Martin Bauer, Philipp Harms, Peter W. Michor. Sobolev metrics on the manifold of all Riemannian metrics. Journal of Differential Geometry 94, 2 (2013), pp. 187-208. arXiv:1102.3347.
FRIAS Project
Stochastic shape analysis and stochastic geometric mechanics
‘The proposed research aims at developing stochastic models for data in nonlinear infinite-dimensional spaces (shape spaces being the prime example) and contributes to a better understanding of the geometry of stochastic processes. It operates within the frameworks of shape analysis and geometric mechanics, which have established themselves as successful tools for handling both non-linearity and infinite-dimensionality, and builds on recently developed stochastic extensions of these methods. Some specific goals are studying singularities of stochastic processes on shape spaces in relation to curvature, developing a variational calculus for stochastic processes which treats drift and volatility as equally important state variables, and bringing these results to applications in shape analysis, hydrodynamics, and mathematical finance.