Stochastic process

cosmos 4th November 2016 at 2:43pm
Non-equilibrium statistical physics Probability theory

Links

Notes on Nonequilibrium StatPhys MT2015 Oxford (mostly stochastic processes)

Nice lecture notes

Discrete Stochastic processes MIT course

Stochastic processes MIT notes

Nice notes on applications of stochastic processes

Wikipedia: Stochastic process

List of stochastic processes topics

Watch: Physics - Physical Applications of Stochastic Processes by Prof. V. Balakrishnan


Stochastic processes

Probability theory

Martingales, Martingales Through Measure Theory

Examples

Classification of models

Descriptions

All these generally are Markov processes

  • Continuous space-time
  • Discrete space
    • Probability description \rightarrow Master equation
      • Discrete time \rightarrow Difference equation. Discrete time master equation.
      • Continuous time \rightarrow Differential Continuous time master equation.
  • Continuous space-discrete time ??. An example is the beginning of the derivation for Brownian motion by Einstein

Important results

  • Dissipation-fluctuation relation. Friction and dissipation are due to the random movements of particles. Fluctuations are too. The coefficients describing them (diffusion coefficient and viscosity) should be related.

Computational methods

Monte Carlo method

Other mathematical aspects

https://en.wikipedia.org/wiki/It%C3%B4_calculus

Applications

Chemistry

Chemical kinetics

Oscillating chemical reactions

Biology

Enzyme kinetics

General phenomena

Number fluctuations

Others

Telegraph noise

Complex systems


Recent paper by Ramin Golestanian (26th Feb 2016): http://pubs.acs.org/doi/pdf/10.1021/acs.nanolett.5b04372 on power spectrum for electric-field-driven ion transport through nanopores. Apparently Pink noise (noise that has power law power spectrum, instead of flat, as for white), is common place in situations with electric fields, and underlying mechanism not totally understood.

https://en.wikipedia.org/wiki/Point_process

Stochastic processes with JS: https://www.npmjs.com/package/stochastic