Exact Moment Scaling from Multiplicative Noise

Details Exact Moment Scaling from Multiplicative Noise Exact Moment Scaling from Multiplicative Noise

2009-11-30

arxiv.org/abs/0911.5662v2

Phys. Rev. E 81, 032102 (2010)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 3 figures. Final version accepted for publication on Phys. Rev. E as Brief Report

Scientific paper

10.1103/PhysRevE.81.032102

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 non trivial time dependence of the microscopic dynamics and we analytically characterize the process evolution, possibly towards a stationary state, and the direct relationship existing between the drift and diffusion coefficients and the time scaling of the moments.

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