Lectures related to Continuous-Time Stochastic Processes: Ergodicism Examples

Stationarity in Stochastic Processes

Explores stationarity in stochastic processes, showcasing how statistical characteristics remain constant over time and the implications on random variables and Fourier transforms.

Probability Distributions in Environmental Studies

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

Explores correlated sampling, weight functions, Markovian chains, ergodicity, and walkers.

Elements of Statistics: Memorylessness, Stationary Processes, Estimation using MLE

Explores memorylessness in distributions, stationary processes, and estimation using MLE.

Introduction to Quantum Chaos

Covers the introduction to Quantum Chaos, classical chaos, sensitivity to initial conditions, ergodicity, and Lyapunov exponents.

Probability and Statistics

Delves into probability, statistics, paradoxes, and random variables, showcasing their real-world applications and properties.

Geostatistics: Analyzing Spatial Data Structures

Covers geostatistics, focusing on spatial data types and their analysis methods.

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.

Stochastic Models for Communications

Covers random vectors, joint probability density, independent random variables, functions of two random variables, and Gaussian random variables.

Stochastic Processes: Review and Properties

Covers the review of random variables, probability density functions, variance, and Gaussian processes.

Stochastic Processes: Symmetric Random Walk

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

Independence and Covariance

Explores independence and covariance between random variables, discussing their implications and calculation methods.

Central Limit Theorem

Covers the Central Limit Theorem and its application to random variables, proving convergence to a normal distribution.

Causal Systems & Transforms: Delay Operator Interpretation

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

Probability and Statistics: Fundamental Theorems

Explores fundamental theorems in probability and statistics, joint probability laws, and marginal distributions.

Probability and Statistics: Fundamentals

Covers the fundamental concepts of probability and statistics, including interesting results, standard model, image processing, probability spaces, and statistical testing.

Modes of Convergence of Random Variables

Covers the modes of convergence of random variables and the Central Limit Theorem, discussing implications and approximations.

Stochastic Models for Communications

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

Law of Large Numbers: Strong Convergence

Explores the strong convergence of random variables and the normal distribution approximation in probability and statistics.

Quantifying Statistical Dependence: Covariance and Correlation

Explores covariance, correlation, and mutual information in quantifying statistical dependence between random variables.