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Institute
- Institut für Mathematik (309) (remove)
Large emissions
(2020)
Pinned Gibbs processes
(2020)
Students of computer science studies enter university education with very different competencies, experience and knowledge. 145 datasets collected of freshmen computer science students by learning management systems in relation to exam outcomes and learning dispositions data (e. g. student dispositions, previous experiences and attitudes measured through self-reported surveys) has been exploited to identify indicators as predictors of academic success and hence make effective interventions to deal with an extremely heterogeneous group of students.
These lecture notes are intended as a short introduction to diffusion processes on a domain with a reflecting boundary for graduate students, researchers in stochastic analysis and interested readers. Specific results on stochastic differential equations with reflecting boundaries such as existence and uniqueness, continuity and Markov properties, relation to partial differential equations and submartingale problems are given. An extensive list of references to current literature is included. This book has its origins in a mini-course the author gave at the University of Potsdam and at the Technical University of Berlin in Winter 2013.
We consider infinite-dimensional diffusions where the interaction between the coordinates has a finite extent both in space and time. In particular, it is not supposed to be smooth or Markov. The initial state of the system is Gibbs, given by a strong summable interaction. If the strongness of this initial interaction is lower than a suitable level, and if the dynamical interaction is bounded from above in a right way, we prove that the law of the diffusion at any time t is a Gibbs measure with absolutely summable interaction. The main tool is a cluster expansion in space uniformly in time of the Girsanov factor coming from the dynamics and exponential ergodicity of the free dynamics to an equilibrium product measure.