A Study of Approximate Descriptions of a Random Evolution




Koepke, Henrike

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We consider a dynamical system that undergoes frequent random switches according to Markovian laws between different states and where the associated transition rates change with the position of the system. These systems are called random evolutions; in engineering they are also known as stochastic switching systems. Since these kinds of dynamical systems combine deterministic and stochastic features, they are used for modelling in a variety of fields including biology, economics and communication networks. However, to gather information on future states, it is useful to search for alternative descriptions of this system. In this thesis, we present and study a partial differential equation of Fokker-Planck type and a stochastic differential equation that both serve as approximations of a random evolution. Furthermore, we establish a link between the two differential equations and conclude our analysis on the approximations of the random evolution with a numerical case study.



stochastic differential equations, switching systems of differential equations, random evolutions