New Approach to Multiplicative Stochastic Processes. I LongTime Statistics and FluctuationSpectrum Theory
Abstract
The fluctuationspectrum analysis for longtime statistical characteristics of the multiplicative stochastic process described by the Langevin equation of motion dr_{t}/dt=(mathit{Delta}beta r_{t}(2}+f_{t})r_{t) , (beta>0, mathit{Delta}>0), f_{t} being the Gaussianwhite noise, is performed by rigorously solving the eigenvalue problem of the extended FokkerPlanck operator H_{q}. This is done by observing how the fluctuation of the coarsegrained average alpha_{t}=t(1}int_0(tr_{s}^{k)) ds reduces as t > infty. Furthermore for mathit{Delta}>0 the scaling behaviors of characteristic functions relevant to the fluctuationspectrum approach are discussed.
 Publication:

Progress of Theoretical Physics
 Pub Date:
 November 1990
 DOI:
 10.1143/ptp/84.5.824
 Bibcode:
 1990PThPh..84..824Y