| The aim of this course is to teach the students the basic modeling and simulation techniques used in applied stochastic analysis. With many vivid examples from science and engineering, the students are expected to grasp the probabilistic ideas and apply them into their own research fields. |
Lect1 Introduction (notes, slides)
Lect2 Random Variables (notes, slides)
Lect3 Generation of Random Variables (notes, slides)
Lect4 Variance Reduction (notes, slides)
Lect5 Limit Theorems (notes, slides)
Lect6 Discrete-Time Markov Chains (notes, slides)
Lect7 Q-Process (slides)
Lect8 Metropolis Algorithm (notes, slides)
Lect9 Multilevel Sampling and KMC (notes, slides)
Lect10 Simulated Annealing and QMC (notes, slides)
Lect11 Random Walk and Brownian Motion (notes, slides, Einstein's 1905 paper)
Lect12 Stochastic Process and Brownian Motion (notes, slides)
Lect13 Construction of BM and Its Properties (notes, slides)
Lect14 SDE and Ito's formula (notes, slides)
Lect15 Connections with PDE (notes, slides)
Lect16 Numerical SDEs: Basics (notes, slides)
Lect17 Numerical SDEs: Advanced Topics (notes, slides)
Lect18 Asymptotic Analysis of SDEs (notes, slides)
Lect19 Path Integral (notes, slides)
Lect20 Applications in Rare Events (notes 1, notes 2, slides)
Lect21 Applications in Chemical Kinetic Systems (notes, slides)