Stochastic Differential Equations and Data-driven Modeling"

Karlstad University

The PhD course includes the following:
- introduction to measure and integration theory (including the Radon-Nikodym theorem, the Lebesgue integral, stochastic integrals)
- introduction to probability theory
- diffusion processes (including Markov processes, Chapman-Enskog processes, ergodicity)
- introduction to stochastic differential equations (SDE), including the Girsanov theorem
- the Fokker-Planck equation
- the Langevin equation
- modeling with SDE (including numerical approximation and parameter estimation for SDE)
- linear response theory (including the Fluctuation-Dissipation theorem, the Green-Kubo formula)

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