Wolfgang Bock

I am quite new at Linnaeus University as I started as Senior Lecturer in August 2023. Since December 2023 I am Docent, which could be translated as Associate Professor in the area of Stochastic Analysis.

I finished my PhD 2013 at the Technische Universität Kaiserslautern in Germany in the field of Stochastic Analysis under the supervision of Martin Grothaus. From August 2013 to August 2014 I was postdoctoral fellow at the Center of Mathematical Analysis and its Applications (CMAF) in Lisbon, Portugal. 

Starting from September 2014 I was on a lecturer position at TU Kaiserslautern and from 2015 I was permanent senior lecturer (Akademischer Rat) and responsible for the Engineering Mathematics in Kaiserslautern. 

During my academic life I have actively participated in several comissions and was also highly involved in internationalization. 

I want to use my knowledge to be a "change maker" and enhance the international visibility of LNU in Stochastic Analysis.  

Teaching

I am currently teaching

1MA441/1MA401 Basic Mathematics for Computer Science/ Mathematics

4MA901 Applied Analysis

Please see MyMoodle for the websites.

Research

Currently my research has 3 focal projects:

1.) Non-Gaussian Analysis and Random Time Change

(with O. Draouil from University of Tunis El Manar and Lorenzo Cristofaro from University of Luxembourg)

Aim is the development of a white noise like calculus for non-Gaussian measures which can be represented as randomly scaled Gaussian measures. Classical examples are Incomplete Gamma measures and the Mittag-Leffler measure. 

The corresponding processes have structural properties which are very close to that of Gaussian processes. We want to use these to develop a regularity theory in the sense of Meyer-Watanabe, based on the Hitsude-Skorokhod type integral. 

2.) Non-Linear Markov Processes and McKean-SDEs

(with M. Louriki (Cadi Ayyad, Morrocco), M. Rehmeier (TU Berlin) and M. Röckner (University of Bielefeld)

Röckner and Rehmeier studied nonlinear Markov processes in the sense of McKean's and present a large class of new examples. Their notion of nonlinear Markov processes is more general in order to include examples of such processes whose one-dimensional time marginal densities solve a nonlinear parabolic PDE. They showed that the associated nonlinear Markov process is given by path laws of weak solutions to a corresponding distribution-dependent stochastic differential equation where both the diffusion and drift coefficient depends singularly (i.e. Nemytskii-type) on its one-dimensional time marginals. 

In this project we lift the theory from the vector-valued to the Gel'fand triple, i.e. infinite dimensional case and establish also a realtionship to a generalized quadratic form. A generalization of McKean-Type was studied by me and M. Louriki for McKean bridges of mean type.

3.) White Noise Analysis and Mittag-Leffler Analysis

In this project, we have serval conributions to the theory of Gaussian Analysis and Mittag-Leffler Analysis. 

• Mosco convergence vs. Hida convergence

In this subproject, I established a sufficient condition for Kuwae-Shioya-Mosco convergence for Dirichlet forms over White Noise spaces. We linked the convergence to a uniform convergence of Hida-distributions. The result is also valid for changing reference measures. As an example we showed that the planar fractional Edwards measure can be used to approximate the stochastic quantization of the planar Brownian polymer measure.

• Operators and Regularity in Mittag-Leffler Analysis

In this subproject we established an operator calculus for non-Gaussian analysis using differential operators on polynomials. The challenge is that there is no Fock space in the Mittag-Leffler case. In addition we worked out concepts for regularity theory in non-Gaussian analysis, which are user friendly.