Skip to content

Fokker-Planck representations of non-Markov Langevin equations: application to delayed systems

Research output: Contribution to journalArticle

Original languageEnglish
Number of pages23
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
DateAccepted/In press - 13 Dec 2018


Noise and time delays, or history-dependent processes, play an integral part of many natural and man-made systems. The resulting interplay between random fluctuations and time non-locality are essential features of the emerging complex dynamics in non-Markov systems. While stochastic differential equations in the form of Langevin equations with additive noise for such systems exist, the corresponding probabilistic formalism is yet to be developed. Here we introduce such a framework via an infinite hierarchy of coupled Fokker-Planck equations for the n-time probability distribution. When the non-Markov Langevin equation is linear, we show how the hierarchy can be truncated at n= 2 by converting the time non-local Langevin equation to a timelocal one with additive coloured noise. We compare the resulting Fokker-Planck equations to an earlier version, solve them analytically and analyse the temporal features of the probability distributions that would allow to distinguish between Markov and non-Markov features.

    Research areas

  • Non-Markov processes, Generalised Langevin equation, Fokker-Planck equation, Delayed Langevin equation, Stochastic systems



  • Full-text PDF (accepted author manuscript)

    Accepted author manuscript, 645 KB, PDF-document

    Embargo ends: 1/01/99

    Request copy

View research connections

Related faculties, schools or groups