arXiv subjects

René Schilling

Publications and source records attributed to René Schilling.

3 recordsLinked to original sources

arXiv2022

Large deviations for stochastic nonlinear systems of slow-fast diffusions with non-Gaussian Lévy noises

We establish the large deviation principle for the slow variables in slow-fast dynamical system driven by both Brownian noises and Lévy noises. The fast variables evolve at much faster time scale than the slow variables, but they are fully inter-dependent. We study the asymptotics of the logarithmic functionals of the slow variables in the three regimes based on viscosity solutions to the Cauchy problem for a sequence of partial integro-differential equations. We also verify the comparison principle for the related Cauchy problem to show the existence and uniqueness of the limit for viscosity solutions.

math.DS↗

arXiv2019

On the Liouville property for non-local Lévy generators

We prove a necessary and sufficient condition for the Liouville property of the infinitesimal generator of a Lévy process and subordinate Lévy processes. Combining our criterion with the necessary and sufficient condition obtained by Alibaud et al., we obtain a characterization of (orthogonal subgroup of the) the set of zeros of the characteristic exponent of the Lévy process.

math.PR↗

arXiv2013

Validity of covariance models for the analysis of geographical variation

Due to the availability of large molecular data-sets, covariance models are increasingly used to describe the structure of genetic variation as an alternative to more heavily parametrised biological models. We focus here on a class of parametric covariance models that received sustained attention lately and show that the conditions under which they are valid mathematical models have been overlooked so far. We provide rigorous results for the construction of valid covariance models in this family. We also outline how to construct alternative covariance models for the analysis of geographical variation that are both mathematically well behaved and easily implementable.

stat.AP↗