Lectures in course MATH-414: Stochastic simulation

Stochastic Simulation: Fundamentals

Introduces stochastic simulation fundamentals, covering course organization, queueing models, finance, statistics, physics, and exam details.

Stochastic Simulation: Introduction and G/G/1 Queueing Model

Covers the stochastic simulations course, G/G/1 queueing model, computational finance, statistics, physics, and Bayesian inference.

Stochastic Simulation: Random Number Generators

Explores random number generators, including Pseudo-RNG algorithms, properties, assessment methods, and independence testing.

Random Number Generators: Properties and Examples

Covers uniform and pseudo-random number generators, properties, examples, and quality assessment through empirical tests.

Conditional Gaussian Generation

Explores the generation of multivariate Gaussian distributions and the challenges of factorizing covariance matrices.

Acceptance-Rejection Methods: Advanced Techniques

Explores advanced techniques in acceptance-rejection methods and sampling from normal distributions.

Generation of Markov Processes

Covers the generation of Markov processes and Markov chains, including transition matrices and stochastic matrices.

Acceptance-Rejection Methods: Advanced Techniques

Explores advanced Acceptance-Rejection methods, sampling from normal distribution, and multivariate random variable generation.

Gaussian Random Vectors: Conditional Generation

Explores generating Gaussian random vectors with specific components based on observed values and explains the concept of positive definite covariance functions in Gaussian processes.

Stochastic Simulation: Markov Processes Generation

Covers the generation of Markov processes and Poisson processes in stochastic simulation.

Wiener Process: Definition and Properties

Explains the definition and properties of the Wiener process, focusing on its covariance function and continuous paths.

Stochastic Simulation: Monte Carlo Method

Covers the properties and error estimates of the Monte Carlo method in stochastic simulation.

Monte Carlo Estimation: Error Analysis

Covers the Monte Carlo method for generating realizations and unbiased estimators.

Stochastic Processes: Generation and Embedding

Explores the generation of stochastic processes, including Gaussian processes, Markov processes, Poisson processes, and circulant embedding.

Markov Chains: Basics and Applications

Introduces Markov chains, covering basics, generation algorithms, and applications in random walks and Poisson processes.

Stochastic Simulation: Variance Reduction Techniques

Explores variance reduction techniques in stochastic simulation, emphasizing the use of auxiliary random variables and sample averages to improve efficiency.

Stochastic Simulation: Computation and Estimation

Covers computation and estimation in stochastic simulation, focusing on generating iid replicas and optimal importance sampling.

Monte Carlo Method: Simulation and Inference

Covers the Monte Carlo method for statistical inferences using simulation tools and sample mean estimators.

Monte Carlo Estimation: Sequential Route Carlo

Explores the Sequential Route Carlo algorithm for Monte Carlo estimation.

Variance Reduction Techniques

Covers variance reduction techniques in stochastic simulation to improve accuracy and efficiency.