Exact Moment Scaling from Multiplicative Noise

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 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.

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

References in corpus (2)

• On the proper reconstruction of complex dynamical systems spoilt by strong measurement noise
• Exact corrections for finite-time drift and diffusion coefficients

Cited by in corpus (4)

• Generalised geometric Brownian motion: Theory and applications to option pricing
• Minimal model of financial stylized facts
• Long-run growth rate in a random multiplicative model
• Multiplicative noise, fast convolution, and pricing