Topic: The Kolmogorov Equations

Transition Semigroups and Infinitesimal Generators for PDEs

The Ornstein-Uhlenbeck Backward Equation

The One-Dimensional Fokker-Planck Equation

The Invariant Density of the Ornstein-Uhlenbeck Process

The Brownian Heat Kernel

Stationary Densities from the Zero-Current Equation

Stationary Densities for Gradient Diffusions

Probability Flux and Boundary Conditions

Ornstein-Uhlenbeck Densities from the Forward Equation

Multidimensional Forward and Backward Equations