Abstract
We construct an equivalent probability description of linear multidelay Langevin equations subject to additive Gaussian white noise. By exploiting the timeconvolutionless transform and a time variable transformation we are able to write a FokkerPlanck equation for the 1time and for the 2time probability distributions valid irrespective of the regime of stability of the Langevin equations. We solve exactly the derived FokkerPlanck equations and analyze the aging dynamics by studying analytically the conditional probability distribution. We discuss explicitly why the initially conditioned distribution is not sufficient to describe fully out a nonMarkov process as both preparation and observation times have bearing on its dynamics. As our analytic procedure can also be applied to linear Langevin equations with memory kernels, we compare the nonMarkov dynamics of a onedelay system with that of a
Generalized Langevin equation with an exponential as well as a power law memory. Application to a generalization of the GreenKubo formula is also presented.
Generalized Langevin equation with an exponential as well as a power law memory. Application to a generalization of the GreenKubo formula is also presented.
Original language  English 

Article number  384002 
Number of pages  29 
Journal  Journal of Physics A: Mathematical and Theoretical 
Volume  49 
Issue number  38 
DOIs  
Publication status  Published  30 Aug 2016 
Structured keywords
 Engineering Mathematics Research Group
Keywords
 NonMarkov
 FokkerPlanck
 Langevin
 aging
 GreenKubo
Fingerprint
Dive into the research topics of 'FokkerPlanck description for a linear delayed Langevin equation with additive Gaussian noise'. Together they form a unique fingerprint.Profiles

Professor Luca Giuggioli
 School of Engineering Mathematics and Technology  Professor of Complexity Sciences
 Animal Behaviour and Sensory Biology
 Ecology and Environmental Change
Person: Academic , Member