Exact moment scaling from multiplicative noise

Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Mar;81(3 Pt 1):032102. doi: 10.1103/PhysRevE.81.032102. Epub 2010 Mar 10.


For a general class of diffusion processes with multiplicative noise, describing a variety of physical as well as financial phenomena, mostly typical of complex systems, we obtain the analytical solution for the moments at all times. We allow for a nontrivial time dependence of the microscopic dynamics and we analytically characterize the process evolution, possibly toward a stationary state, and the direct relationship existing between the drift and diffusion coefficients and the time scaling of the moments.

MeSH terms

  • Computer Simulation
  • Data Interpretation, Statistical*
  • Diffusion*
  • Models, Chemical*
  • Models, Statistical*