Lectures related to Stochastic process

Probability Distributions in Environmental Studies

Explores probability distributions for random variables in air pollution and climate change studies, covering descriptive and inferential statistics.

Rainfall Models: Deterministic vs Stochastic

Covers deterministic and stochastic rainfall models in water resources engineering, including generation, calibration, and spatially explicit models.

Fourier Transform and Spectral Densities

Covers the Fourier transform, spectral densities, Wiener-Khinchin theorem, and stochastic processes.

Wiener Process: Definition and Properties

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

Martingale-based Methods for Stochastic Systems

Explores martingales in stochastic systems, focusing on formal analysis, termination analysis, and stability verification.

Signal Processing Fundamentals

Explores signal processing fundamentals, including discrete time signals, spectral factorization, and stochastic processes.

Stochastic Calculus: Itô's Formula

Covers Stochastic Calculus, focusing on Itô's Formula, Stochastic Differential Equations, martingale properties, and option pricing.

Stochastic Processes: Symmetric Random Walk

Covers the properties of the symmetric random walk in stochastic processes.

Sub- and Supermartingales: Theory and Applications

Explores sub- and supermartingales, stopping times, and their applications in stochastic processes.

Stochastic Calculus: Brownian Motion

Explores stochastic processes in continuous time, emphasizing Brownian motion and related concepts.

Controlled Stochastic Processes

Explores controlled stochastic processes, dynamic programming, and the Machine Replacement Problem.

Asset Selling: Optimal Revenue Policy

Explores asset selling dynamics, optimal revenue policy, acceptance thresholds, and commodity price impact.

Response Theory and Phase Transitions

Explores response theory, phase transitions, and fluctuations in weakly interacting systems, including stochastic particles and opinion formation models.

Stochastic Games on Directed Networks

Covers linear-quadratic stochastic differential games on directed chain networks and open-loop Nash equilibria.

Fokker-Planck Equation: Derivations and Applications

Explores the derivation of the Fokker-Planck equation and its applications in stochastic differential equations.

Stochastic Simulation: Variance Reduction Techniques

Covers stochastic simulation and variance reduction techniques, focusing on Courra variate and auxiliary distribution generation.

Stochastic Models for Communications

Covers stochastic models for communications, focusing on random variables, Markov chains, Poisson processes, and probability calculations.

Stochastic Models for Communications: M/G/infinity Queue

Explores the M/G/infinity queue model for systems with infinite capacity and general service times.

Stochastic Models for Communications: Continuous-Time Stochastic Processes Examples 4-5

Covers examples of continuous-time stochastic processes in communication systems.

Applied Probability and Stochastic Processes: Tutorial 02

Covers communicating classes, hitting time, probabilities, and the Gambler's Ruin Model in stochastic processes.