Density Evolution
From the book
Chapter 19: Stochastic Differential Equations. In the chapter mind map this icon labels Probability Evolution: Fokker-Planck Preview. The discussion below is excerpted and lightly edited from § Probability Evolution Viewpoint in Mathematics for AI and Machine Learning. Related material also appears in Chapter 21 (Paths vs Densities: Three Levels of Description), Chapter 21 (Determinism of Prob Distributions).
- A path distribution
- A time-indexed density $p_t(\mathbf{x})$
This leads to the Fokker–Planck equation (the matrix chapter).
What this drawing shows
What you see. Shows a probability density $p(x,t)$ spreading and flattening under Fokker–Planck diffusion from $t_0$ to $t_1$.
In the mind map. Chapter 19 — Probability Evolution: Fokker-Planck Preview. See From the book above for definitions, figures, and worked examples.
Also appears in Ch. 21 (Paths vs Densities: Three Levels of Description); Ch. 21 (Determinism of Prob Distributions).
Where to read next
Read the full definitions, figures, and worked examples in Chapter 19: Stochastic Differential Equations — see the mind-map node Probability Evolution: Fokker-Planck Preview.
This concept is also referenced in Chapter 21 (Paths vs Densities: Three Levels of Description); Chapter 21 (Determinism of Prob Distributions).
