The course gives an advanced treatment of the theory of stochastic processes based on probability theory and mathematical analysis.Hence there is a certain focus on proofs and rigour, instead of reasoning and learning by means of applications and examples. As well as being suitable for students with a more theoretical interest, the course is suitable for gaining deepened knowledge of stochastic processes for applied students with a background from one of the courses MSG800 Basic Stochastic Processes, MSG860 Basic Stochastic Processes F.
What is a stochastic process? Distribution theory. Time series with random walks. Brownian motion and diffusions. Elements of Levy processes. Gaussian processes. Stationarity and weak stationarity. Continuous time Markov chains. Elements of Queues. Self-similar processes. Elements of filtering and forecasting. Elements of simulation and numerical methods.