Exact moment scaling from multiplicative noise.
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.
Bormetti
Giacomo
G
CeRS-IUSS, Vle Lungo Ticino Sforza 56, Pavia 27100, Italy. giacomo.bormetti@pv.infn.it
Delpini
Danilo
D
D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D004058:Diffusion; D008956:Models, Chemical; D015233:Models, Statistical