Lectures related to Poisson Process Theory: Properties and Applications

Simulation & Optimization: Poisson Process & Random Numbers

Explores simulation pitfalls, random numbers, discrete & continuous distributions, and Monte-Carlo integration.

Gaussian Process: Covariance and Correlation Functions

Explores Gaussian processes, covariance functions, intrinsic stationarity, and extreme applications in statistics.

Mapping and Colouring: Poisson Processes

Covers the theorems of superposition and colouring for Poisson processes.

Estimating R: Marking and Convergence

Covers the estimation of R in Poisson processes, focusing on marking points and convergence.

Estimating R: Theory of Poisson Processes

Covers the theory of Poisson processes and the estimation of the intensity parameter R.

Poisson Process Mapping

Explains how q = rw defines a Poisson process and its intensity.

Point Processes: Spatial Analysis

Explores point processes in spatial analysis, focusing on spatial object dissemination and pattern detection.

Point Processes: Convergence and Gaussian Processes

Covers point processes, convergence criteria, Laplace functionals, Gaussian processes, covariance functions, and intrinsic stationarity.

Multivariate Extremes: Applications and Dependence

Explores multivariate extremes, including overwhelming sea defenses and heat waves.

Point Processes: Extremal Limit Theorems

Explores the theory of point processes and their applications to extremes, emphasizing the Laplace functional and Kallenberg's theorem.

Stochastic Simulation: Markov Processes Generation

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

Extreme Value Theory: Point Processes

Covers the application of extreme value theory to point processes and the estimation of extreme events from equally-spaced time series.

Poisson Processes Theorems

Discusses important theorems related to Poisson processes and their applications in analyzing exceedances and likelihood.

Mapping Theorems: Poisson Processes and Intensity Functions

Explores mapping theorems for Poisson processes and their intensity functions.

Point Processes: Extreme Value Theory

Explores point processes in extreme value theory, focusing on modeling exceedances and the theory behind point patterns.

Poisson Process Approach

Explores the Poisson process approach in extreme value analysis, emphasizing component-wise transformations and likelihood functions for extreme events.

Simulation: Control of Dynamic Systems

Explores simulation of common structures and control of dynamic systems through friction and elasticity constants.

Asymptotic Independence Models

Explores extremal limit theorems, statistical analysis, and asymptotic independence models for rare events.

Extreme Statistics: Threshold Models

Covers the theory and applications of extreme statistics, focusing on threshold models for analyzing extremes of time series.

Stochastic Calculus: Lecture 1

Covers the essentials of probability, algebras, and conditional probability, including the Borel o-algebra and Poisson processes.