# Research at Mathematical Statistics

## Torkel Erhardsson

Ph.D.,doc, docent, senior lecturer

Construction of explicit error bounds in distributional approximations, in particular approximations with Poisson and compound Poisson distributions, using Stein's method and couplings. Applications of such bounds to the distribution of the number of entries of a stochastic process into a rare subset of the state space, in particular to stationary Markov, semi-Markov, or regenerative processes. Adaptation of Stein's method to new classes of distributions. The theory and applications of Bayesian inference, in particular nonparametric Bayesian inference for measures.

## Mikhail Lifshits

Dr. of Math. Sciences, guest professor:

My research domain is the theory of random processes with special emphasis on Gaussian processes, and large or small deviation probabilities. I am particularly interested in connections between the properties of random processes and those of linear operators. Most recently I have worked as well on the approximation of random processes (including random fields of high parametric dimension) and on some optimal pursuit problems. I am also interested in the limit theorems for "teletraffic models" described in my recent book "Random Processes by Example" (World Scientific, 2014).

## Jörg-Uwe Löbus

Dr. rer. nat. habil., docent, senior lecturer:

My research concerns stochastic analysis and applications such as particle systems and diffusion processes. I am particularly interested in infinite dimensional stochastic calculus. Most recently I have worked on Mosco type convergence as well as weak convergence of stochastic processes and particle systems, and on quasi-invariance of probability measures under certain stochastic and non-stochastic flows. Particle approximations of solutions to certain PDEs play a role in my work.

## Martin Singull

Ph.D.,doc, senior lecturer:

My research interest is multivariate statistics, focusing on multivariate (vector-) normal distribution with a patterned covariance matrix, for example a covariance matrix with a banded structure. I have also considered a Growth Curve model (bilinear regression) with a linearly structured covariance matrix, e.g., banded, Toeplitz, special structure with zeros or some mix. Right now, I am working on a Kronecker structured covariance matrix which leads to a matrix normal distribution or more greneral the multilinear normal distribution, i.e., a tensor normal distribution. The Kronecker structured model can for example be used in the purpuse to model dependent multilevel observations.

## Xiangfeng Yang

Ph. D., senior lecturer:

Various aspects in limit theorems of stochastic processes and their applications in partial integro-differential equations: precise weak convergence of infinitely divisible processes, precise large deviations of (jump) Markov processes, rough large deviations of bridge processes (such as generalized Brownian bridges, Levy bridges, Bernstein bridges, etc.), estimations on upper tail probabilities of Gaussian processes (such as integrated Brownian motions, random series, etc.), persistence of random walks, probabilities of hitting convex hulls generated by random vectors.

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Last updated: Tue Sep 05 11:44:07 CEST 2017