Application of the Fokker-Planck equation

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SUMMARY

The Fokker-Planck equation is a partial differential equation that describes the time evolution of the probability density function of a particle's velocity under the influence of drag and random forces, particularly in contexts like Brownian motion. This equation is applicable in various fields, including diffusion MRI and mathematical finance, where it models the evolution of probability distributions. Understanding its applications can enhance insights into complex systems influenced by stochastic processes. The discussion highlights the need for practical examples beyond traditional contexts, such as water molecules in MRI.

PREREQUISITES
  • Understanding of partial differential equations
  • Familiarity with stochastic processes
  • Basic knowledge of Brownian motion
  • Introduction to mathematical finance concepts
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  • Research applications of the Fokker-Planck equation in diffusion MRI
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Engineers, physicists, mathematicians, and finance professionals interested in the applications of the Fokker-Planck equation in modeling complex systems and probability distributions.

alecrimi
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Hallo everybody.
Foreword1: I am an engineer not a physicist
Foreword2: I am reading a paper about diffusion MRI who refers to harmonic oscillator hamiltonian.

The paper sometimes mention the Fokker Planck equations. Now, I don't want yet understand the relationshipt between diffusion-hamiltonian and Fokker-Planck, but I will be happy to understand the common purpose to use Fokker-Planck equations.

The definition is : partial differential equations that describes the time evolution of the probability density function of the velocity of a particle under the influence of drag forces and random forces, as in Brownian motion. Can you give me simple applications when we need to model the evolution of hte pdf under the influence of forces as in Brownian motion (possibly different from water molecules in MRI)?
 
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