This course presents the mathematical foundations of Probability Theory, including the concepts of Probability Space and random variable. Various types of convergence of sequences and measurable ...

Probability theory forms the mathematical backbone for quantifying uncertainty and random events, providing a rigorous language with which to describe both everyday phenomena and complex scientific ...

Probability theory has long provided a rigorous framework for quantifying uncertainty, yet its extension to infinite sets introduces profound conceptual challenges and opportunities. Contemporary ...

In this article, we prove that the measures ℚ T associated to the one-dimensional Edwards' model on the interval [0, T] converge to a limit measure ℚ when T goes to infinity, in the following sense: ...

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 ...

We discuss issues of existence and stochastic modeling in regard to sequences that exhibit combined features of independence and instability of relative frequencies of marginal events. The concept of ...

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 ...

We will start by embedding probability theory into a general framework, where we will construct infinite sequences of independent random variables, and (re)visit laws of large numbers, 0-1 laws and ...