## ST115 : Introduction to Probability - Term 2, 2022

There are a number of real-world phenomena whose outcome cannot be determined in advance with certainty but on which we would anyway like to be able to make quantitative predictions. This is what Probability Theory is for.

As the name of the course suggests, in the following weeks we will lay the foundations of modern Probability Theory and see how it can be used to measure the likeliness of certain events. Topics we will cover include the axioms of Probability, basic Combinatorics, conditional probability, independence, random variables and their distributions, expectation and variance. At the end of the course, we will see some of the most basic and beautiful limit theorems that make Probability Theory so powerful.

For more information, please consult this link or the moodle page.

As the name of the course suggests, in the following weeks we will lay the foundations of modern Probability Theory and see how it can be used to measure the likeliness of certain events. Topics we will cover include the axioms of Probability, basic Combinatorics, conditional probability, independence, random variables and their distributions, expectation and variance. At the end of the course, we will see some of the most basic and beautiful limit theorems that make Probability Theory so powerful.

For more information, please consult this link or the moodle page.

## ST112 : Probability B - Term 2, 2021

This course is a continuation of ST111 Probability A and the goal is to provide an introduction to the basic tools on which Probability Theory is based. After reviewing the notion of random variable and its distribution, we will define independence, expectation, and variance. Once these concepts are put in place, we will use them to discuss the celebrated law of large number and central limit theorem.

For more information, please consult this link or the moodle page.

For more information, please consult this link or the moodle page.

## Introduction to Stochastic PDEs - Term 1, 2019

This course will be an introduction to stochastic partial differential equations (SPDEs). After providing some background on functional analysis and infinite dimensional Gaussian measures, we will turn to stochastic integration in infinite dimensions. The last part of the course will be dedicated to the analysis of some linear and semi-linear SPDEs.

**Instructors:**Giuseppe Cannizzaro and Ajay Chandra.**Further information available at**__https://www.randomsystems-cdt.ac.uk/core-courses__**Lecture Notes:**, Motivation: PAM equation, SHE; preliminaries on Gaussian measures on Banach spaces. (Ajay)__Lecture 1__, Fernique's theorem and its consequences; Kolmogorov's continuity theorem. (Giuseppe)__Lecture 2__, Cameron-Martin space, Reproducing kernel Hilbert space. (Ajay)__Lecture 3__, Cameron-Martin theorem, support of Gaussian measures, images of Gaussian measures. (Ajay)**Lecture 4**, Cylindrical Wiener process, stochastic integration in infinite dimensions. (Giuseppe)**Lecture 5****Lecture**, Semigroup Theory: Strongly continuous and analytic semigroups. (Giuseppe)**6**, Linear SPDEs with additive noise: existence, uniqueness and regularity of solutions. (Ajay)**Lecture 7**, Semilinear SPDEs with additive noise: local existence and uniqueness; examples. (Giuseppe)**Lecture 8**

**Assessment:**Please register online at__bit.ly/SPDECourse2019Projects__