Probability

Program Description

Probability theory is the branch of mathematics concerned with the analysis of random phenomena. The members of the ISM Probability Group are involved in research in a broad range of areas spanning theoretical and applied, continuous and discrete probability. A particular focus is on the development and analysis of probabilistic models for real-world phenomena from physics, biology, statistics and computer science. Some specific topics of interest are: statistical physics in a random environment, branching systems in biology, distances and random energy landscapes, data structure analysis using random trees, genetics and population biology.

Many members of the group are also members of the CRM Probability Lab.

Program Members

Academic Program

Students interested in graduate study in any of the areas cited above are invited to apply for admission to the program. There are no formal prerequisites other than those required by the departments. The following guidelines should be followed, however, and courses selected in consultation with an advisor from the group.

Students in the program are expected to have mastered the subject matter of the undergraduate curriculum in probability theory. All students are required to take the basic courses: Real Analysis Measure Theory and Probability Theory. Students are then expected to take a number of more specialized courses.

2017-18 Course Listings

Fall

Advanced Probability Theory 1

Probability spaces. Random variables and their expectations. Convergence of random variables in Lp. Independence and conditional expectation. Introduction to Martingales. Limit theorems including Kolmogorov's Strong Law of Large Numbers.

Prof. Linan Chen

MATH 587

Institution: McGill University

Probabilités - Université de Montréal

Espace de probabilité, variables aléatoires, indépendance, espérance mathématique, modes de convergence, lois des grands nombres, théorème central limite, espérance conditionnelle et martingales.

Prof. Sabin Lessard

MAT 6717

Institution: Université de Montréal

Winter

Honours Stochastic Processes

Conditional probability and conditional expectation, generating functions. Branching processes and random walk. Markov chains:transition matrices, classification of states, ergodic theorem, examples. Birth and death processes, renewal theory, queueing theory. Poisson processes. Introduction to Brownian motion, martingales. Further topics as time permits.

Prof. Louigi Addario-Berry

MATH 547

Institution: McGill University

Calcul stochastique

Le cours se veut une introduction aux processus stochastiques avec un accent sur les martingales, le mouvement brownien et l'intégrale stochastique. Ces trois objets mathématiques sont omniprésents de nos jours en probabilités et en finance-mathématique.
Le cours MAT6717 ou l'équivalent (c'est-à-dire un cours de probabilités utilisant de la théorie de la mesure) est un pré-requis. 
Les objectifs principaux du cours sont: 
1) explorer les propriétés du mouvement brownien et des martingales en général;
2) Développer des outils tels que l'intégrale stochastique d'Itô pour étudier et construire des processus stochastiques ;
3) Appliquer ces outils à la résolution de problèmes (formule de Black Scholes, équations différentielles stochastique, théorèmes de représentation des martingales, théorèmes de Girsanov).

Prof. Alexander Fribergh

MAT 6798

Institution: Université de Montréal