- Understand and apply the concept of conditional expectation and its properties ;
- Know fundamental properties of stochastic processes;
- Model time dependent random experients with discrete states using Markov chains and study their properties;
- Know several possibilities to construct the Poisson process;
- Model with the Poisson prcocess, e.g., for application problems in insurance mathematics;
- Understand Gaussian processes, in particular the Wiener process and its properties;
- Comprehend the Markov property and Chapman-Kolmogoroc equation for stochastic processes;
- Investigate stochastic processes for the martingale property;
- Know and understand martingale convergence theorems.
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Conditional expectation, stochastic processes, Markov chains, Poisson process, Wiener process, Markov property, Chapman-Kolmogorov equation, martingale, martingale convergence theorems
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