| 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)
Lect2 Random Variables (notes)
Lect3 Generation of Random Variables (notes)
Lect4 Variance Reduction (notes)
Lect5 Limit Theorems (notes)
Lect6 Markov Chains (notes)
Lect7 Metropolis Algorithm (notes)
Lect8 Multilevel Sampling and KMC (notes)
Lect9 Simulated Annealing and QMC (notes)
Lect10 Random Walk and Brownian Motion (notes)
Lect11 Stochastic Processes and Brownian Motion (notes)
Lect12 Construction of Brownian Motion (notes)
Lect13 SDE and Ito's formula (notes)
Lect14 Connections with PDE (notes)
Lect15 Numerical SDEs: Basics (notes)
Lect16 Numerical SDEs: Advanced Topics (notes)
Lect17 Path Integral (notes)
Lect18 Applications in Chemical Kinetic Systems (notes)