The Fokker-Planck equation, and stationary densities

TL;DR

This paper explores the Fokker-Planck equation for local Markovian stochastic models, examining cases with uncorrelated initial states and studying one-dimensional fields with kink-solutions.

Contribution

It provides a detailed analysis of the Fokker-Planck equation in various special cases and introduces the study of local interactions with kink-solutions in one-dimensional fields.

Findings

Uncorrelated initial states can remain uncorrelated under certain conditions.

The Fokker-Planck equation describes the evolution of local Markovian stochastic models.

Identification of kink-solutions in one-dimensional local interaction fields.

Abstract

The most general local Markovian stochastic model is investigated, for which it is known that the evolution equation is the Fokker-Planck equation. Special cases are investigated where uncorrelated initial states remain uncorrelated. Finally, stochastic one-dimensional fields with local interactions are studied that have kink-solutions.