We show that the total variational distance between a process of two particles interacting by exclusion and a process of two independent particles goes to 0 as time goes to infinity, when the ...

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 ...

Random walks constitute one of the most fundamental models in the study of stochastic processes, representing systems that evolve in a sequence of random steps. Their applications range from modelling ...

Introduction to probability theory and statistical methods necessary for analyzing the behavior of processes and experiments. Statistical tests for detecting significant changes in process parameters.

Let X t be an α-self-similar Markov process on (0, ∞) killed when hitting 0. α-self-similar extensions of X(t) to [ 0, ∞) are studied via Itô execusion theory (entrance laws). We give a condition that ...

The law of large numbers is not an optional belief.

This course is compulsory on the BSc in Actuarial Science, BSc in Actuarial Science (with a Placement Year), BSc in Financial Mathematics and Statistics and BSc in Mathematics, Statistics and Business ...