SkillsAt the conclusion of the course students are expected to be able to:
KnowledgeIn this course, the basic tools to analyse stochastic phenomena are introduced by using the diffusion process as one of the most useful examples of stochastic process. The topics include Langevin equations, Fokker-Planck equations, first passage problems, and master equations. The tools are then used to analyze selected stochastic models that have wide applications to various real phenomena. The topics are chosen from non-equilibrium stochastic phenomena, including geometric Brownian motion (used in e.g. modeling finance), birth and death process (used in e.g. chemical reactions and population dynamics), and asymmetric simple exclusion process (used in e.g. traffic jam formation). Throughout the course, exercises for analytical calculations and numerical simulations are provided to improve the students' skills.
CompetencesThis course will provide the students with mathematical tools that have application in range of fields within and beyond physics. Examples of the fields include non-equilibrium statistical physics, biophysics, soft-matter physics, complex systems, econophysics, social physics, chemistry, molecular biology, ecology, etc. This course will provide the students with a competent background for further studies within the research field.
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Publication of new courses All planned PhD courses at the PhD School are visible in the course catalogue. Courses are published regularly.