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.

Exact moment scaling from multiplicative noise / Bormetti, G; Delpini, Danilo. - In: PHYSICAL REVIEW E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS. - ISSN 1539-3755. - 81:3(2010), pp. 032102.032102-1-032102.032102-4. [10.1103/PhysRevE.81.032102]

Exact moment scaling from multiplicative noise

DELPINI, Danilo
2010

Abstract

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11388/79230
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