Search

Summary

At the mesoscale, the fluctuating phenomena are described using the theory of stochastic processes. Depending on the random variables, different stochastic processes can be defined. The properties of stationarity, reversibility, and Markovianity are defined and discussed. The classes of discrete- and continuous-state Markov processes are presented including their master equation, their spectral theory, and their reversibility condition. For discrete-state Markov processes, the entropy production is deduced and the network theory is developed, allowing us to obtain the affinities on the basis of the Hill–Schnakenberg cycle decomposition. Continuous-state Markov processes are described by their master equation, as well as stochastic differential equations. The spectral theory is also considered in the weak-noise limit. Furthermore, Langevin stochastic processes are presented in particular for Brownian motion and their deduction is carried out from the underlying microscopic dynamics.

A definition of the Markovian property is given for a lattice process and a Gaussian Markovian lattice process is constructed on a torus lattice. From this a Gaussian Markovian process is constructed for a lattice in the plane and its properties are studied.

Search Results

Refine search

Refine search

Actions for selected content:

2 results

4 - Stochastic Processes

Summary

A Gaussian Markovian process on a square lattice

Search Results

Refine search

Refine search

Actions for selected content:

Save Search

2 results

4 - Stochastic Processes

Summary

A Gaussian Markovian process on a square lattice