Lectures related to Brownian Motion: Fundamentals and Applications

Fourier Transform and Spectral Densities

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

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

Stochastic Processes: Brownian Motion

Explores Brownian motion, Langevin equations, and stochastic processes in physics.

White Noise Form of the Langevin Equation

Covers the white noise form of the Langevin equation and its applications.

Causal Systems & Transforms: Delay Operator Interpretation

Covers z Variable as a Delay Operator, realizable systems, probability theory, stochastic processes, and Hilbert Spaces.

Brownian Motion: From Molecules to Cells

Explores the core concepts of Brownian motion, from molecules to cells, including its history, hypothesis versus description, Langevin's solution, and methods for measuring Brownian motion.

Harmonic Signals and Spectrum Estimation

Explores harmonic signals, spectrum estimation, and signal analysis methods using MATLAB tools.

Maximum Entropy Principle: Stochastic Differential Equations

Explores the application of randomness in physical models, focusing on Brownian motion and diffusion.

Fokker-Planck Equations

Explores Fokker-Planck equations, escape rates, and first passage time analysis in statistical physics.

Langevin dynamics: Path Integral Methods

Covers Langevin dynamics, Fokker-Planck equation, solving the Langevin equation, and efficiency of Langevin sampling in molecular dynamics.

Stochastic Processes and Spectral Densities

Covers spectral densities, signal correlations, and white noise processes in stochastic systems.

Parseval Relations and Fourier Transform

Covers Parseval relations, Fourier series, energy calculation, and correlation in signal processing.

Probability and Stochastic Processes: Fundamentals and Applications

Discusses the fundamentals of probability and stochastic processes, focusing on random variables, their properties, and applications in statistical signal processing.

Properties of Time-Frequency Domain Signals

Covers the main properties of time-frequency domain signals and their limitations.

Stochastic Calculus: Brownian Motion

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

Stochastic Calculus: Itô's Formula

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

Yule Walker Equations: Efficient Implementation and Correlation Analysis

Explores Yule Walker equations for efficient implementation and correlation analysis in signal processing.

Stochastic Calculus: Integrals and Processes

Explores stochastic calculus, emphasizing integrals, processes, martingales, and Brownian motion.

Martingales and Brownian Motion

Discusses convergence, martingales, Brownian motion, joint laws, testing procedures, and stop times.

Signal Processing: Correlation and Spectral Density

Delves into correlation and spectral density of signals, explaining their significance and applications.