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Martin Büttner

Publications and source records attributed to Martin Büttner.

5 recordsLinked to original sources
arXiv2019

On the monotone stability approach to BSDEs with jumps: Extensions, concrete criteria and examples

We show a concise extension of the monotone stability approach to backward stochastic differential equations (BSDEs) that are jointly driven by a Brownian motion and a random measure for jumps, which could be of infinite activity with a non-deterministic and time inhomogeneous compensator. The BSDE generator function can be non convex and needs not to satisfy global Lipschitz conditions in the jump integrand. We contribute concrete criteria, that are easy to verify, for results on existence and uniqueness of bounded solutions to BSDEs with jumps, and on comparison and a-priori $L^{\infty}$-bounds. Several examples and counter examples are discussed to shed light on the scope and applicability of different assumptions, and we provide an overview of major applications in finance and optimal control.

math.PR↗
arXiv2017

Directional spin wavelets on the sphere

We construct a directional spin wavelet framework on the sphere by generalising the scalar scale-discretised wavelet transform to signals of arbitrary spin. The resulting framework is the only wavelet framework defined natively on the sphere that is able to probe the directional intensity of spin signals. Furthermore, directional spin scale-discretised wavelets support the exact synthesis of a signal on the sphere from its wavelet coefficients and satisfy excellent localisation and uncorrelation properties. Consequently, directional spin scale-discretised wavelets are likely to be of use in a wide range of applications and in particular for the analysis of the polarisation of the cosmic microwave background (CMB). We develop new algorithms to compute (scalar and spin) forward and inverse wavelet transforms exactly and efficiently for very large data-sets containing tens of millions of samples on the sphere. By leveraging a novel sampling theorem on the rotation group developed in a companion article, only half as many wavelet coefficients as alternative approaches need be computed, while still capturing the full information content of the signal under analysis. Our implementation of these algorithms is made publicly available.

cs.IT↗
arXiv2016

Wavelet reconstruction of E and B modes for CMB polarisation and cosmic shear analyses

We present new methods for mapping the curl-free (E-mode) and divergence-free (B-mode) components of spin 2 signals using spin directional wavelets. Our methods are equally applicable to measurements of the polarisation of the cosmic microwave background (CMB) and the shear of galaxy shapes due to weak gravitational lensing. We derive pseudo and pure wavelet estimators, where E-B mixing arising due to incomplete sky coverage is suppressed in wavelet space using scale- and orientation-dependent masking and weighting schemes. In the case of the pure estimator, ambiguous modes (which have vanishing curl and divergence simultaneously on the incomplete sky) are also cancelled. On simulations, we demonstrate the improvement (i.e., reduction in leakage) provided by our wavelet space estimators over standard harmonic space approaches. Our new methods can be directly interfaced in a coherent and computationally-efficient manner with component separation or feature extraction techniques that also exploit wavelets.

astro-ph.CO↗
arXiv2014

On spin scale-discretised wavelets on the sphere for the analysis of CMB polarisation

A new spin wavelet transform on the sphere is proposed to analyse the polarisation of the cosmic microwave background (CMB), a spin $\pm 2$ signal observed on the celestial sphere. The scalar directional scale-discretised wavelet transform on the sphere is extended to analyse signals of arbitrary spin. The resulting spin scale-discretised wavelet transform probes the directional intensity of spin signals. A procedure is presented using this new spin wavelet transform to recover E- and B-mode signals from partial-sky observations of CMB polarisation.

astro-ph.IM↗