CATALOG DESCRIPTION: Fundamentals of random variables; mean-squared estimation; limit theorems and convergence; definition of random processes; autocorrelation and stationarity; Gaussian and Poisson ...

Probability theory constitutes the mathematical framework for quantifying uncertainty and analysing random phenomena. Its foundations lie in measure theory, where a probability space is defined as a ...

We study the tail behavior of regularly varying infinitely divisible random vectors and additive processes, i.e. stochastic processes with independent but not necessarily stationary increments. We ...

Stochastic differential equations (SDEs) and random processes form a central framework for modelling systems influenced by inherent uncertainties. These mathematical constructs are used to rigorously ...

Explain why probability is important to statistics and data science. See the relationship between conditional and independent events in a statistical experiment. Calculate the expectation and variance ...

We study a one-dimensional telegraph process $(M_t)_t \geq 0$ describing the position of a particle moving at constant speed between Poisson times at which new velocities are chosen randomly. The ...

This course is available on the MSc in Applicable Mathematics, MSc in Financial Mathematics and MSc in Quantitative Methods for Risk Management. This course is available as an outside option to ...

This course is available on the MSc in Financial Mathematics, MSc in Mathematics and Computation and MSc in Quantitative Methods for Risk Management. This course is available with permission as an ...