Stochastic analysis today imposes itself as an essential discipline for modeling and understanding random phenomena evolving in continuous time. Whether it concerns the behavior of financial markets, turbulence in quantum mechanics, or weather fluctuations, this mathematical universe allows for the formalization of complex processes through rigorous tools. At the heart of this theory, Itô integrals … Read more
In short: Foundations and definitions of geometric probabilities in measurable spaces Geometric probabilities represent an essential branch of contemporary probabilistic theories, focusing on the measurement of events within continuous spaces. Unlike classical probabilities based on counting outcomes, they involve a rigorous measure of subsets in often vector or metric spaces, particularly within measurable spaces. This … Read more
In the vast landscape of physics, the understanding of matter at the microscopic scale has long been dominated by classical statistical mechanics. Based on the Boltzmann-Gibbs entropy, this approach has allowed for an astonishingly precise explanation of the thermodynamic behavior of many systems. Yet, in the face of the growing complexity of natural systems, particularly … Read more
IN BRIEF Origins of probability theory in games of chance. 1654: Correspondence between Pierre de Fermat and Blaise Pascal marking the beginning of probability calculus. Development of probabilities during the 19th century. Kolmogorov introduced axiomatic in 1933. Abraham de Moivre and his contribution with “The Doctrine of Chances” in 1718. Probability theory was systematized from … Read more