First, we discuss basic probability notions from the viewpoint of category theory. Our approach is based on the following four "sine quibus non" conditions: 1. (elementary) category theory is ...

We will begin with a thorough review of basic probability theory including probability spaces, random variables, probabilistic inequalities, and laws of large numbers. We then will study a number of ...

The Annals of Probability, Vol. 2, No. 1 (Feb., 1974), pp. 51-75 (25 pages) This paper is part of the constructive program, initiated by E. Bishop, of systematic examination of classical mathematics ...

The purposes of this course are (a) to explain the formal basis of abstract probability theory, and the justification for basic results in the theory, and (b) to explore those aspects of the theory ...

Stochastic analysis is a fundamental branch of probability theory which is linked to diverse areas of mathematics (e.g. partial differential equations, mathematical physics, geometry) and finds ...

The course covers the probability, distribution theory and statistical inference needed for third year courses in statistics and econometrics. Michaelmas term: Events and their probabilities.

Introduces students to the tools methods and theory behind extracting insights from data. Covers algorithms of cleaning and munging data, probability theory and common distributions, statistical ...

Course syllabus: We will start by developing the theory of Markov chains further, explore their relations to martingales and give applications to the solution of Dirichlet problem and maximum (resp.