Lectures related to Fokker-Planck Equation: Derivations and Applications

Maximum Entropy Principle: Stochastic Differential Equations

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

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

Stochastic Differential Equations

Covers Stochastic Differential Equations, Wiener increment, Ito's lemma, and white noise integration in financial modeling.

Fourier Transform and Spectral Densities

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

White Noise Form of the Langevin Equation

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

Langevin dynamics: Path Integral Methods

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

Stochastic Calculus: Lecture 1

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

Stochastic Calculus: Brownian Motion

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

Stochastic Calculus: Integrals and Processes

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

Stochastic Processes: Brownian Motion

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

Fokker-Planck & KPZ Equations

Explores the Fokker-Planck and KPZ equations in stochastic processes and random growth models.

Girsanov's Theorem: Numerical Simulation of SDEs

Covers Girsanov's Theorem, absolutely continuous measures, and numerical simulation of Stochastic Differential Equations (SDEs) with applications in finance.

Stochastic Calculus: Interest Rate Models

Provides an overview of stochastic calculus and its applications in interest rate models and financial modeling.

Spatial Ergodicity for SPDEs

Explores spatial ergodicity for SPDEs, covering basic formulations, initial data effects, and results on ergodicity and CLT.

Stochastic Differential Equations: Examples and Relations

Explores Stochastic Differential Equations with examples like Brownian Motion and Square-Root Processes, discussing their relation to Partial Differential Equations.

Sub- and Supermartingales: Theory and Applications

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

Probability Distributions in Environmental Studies

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

Wiener Process: Definition and Properties

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

Stochastic Integral: Isometry Continuity

Covers stochastic integrals, emphasizing isometry and continuity properties in martingales and different spaces.

Stochastic Reaction Simulation: Constantin

Covers the algorithm to simulate molecule reactions using random numbers.