Spongy-Bone
发表于 2025-3-25 06:45:59
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overwrought
发表于 2025-3-25 09:12:50
Stochastic Systems with Time Delay978-3-030-80771-9Series ISSN 2190-5053 Series E-ISSN 2190-5061
CUR
发表于 2025-3-25 13:57:02
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鲁莽
发表于 2025-3-25 15:48:39
Infinite Fokker-Planck Hierarchyderstand the non-Markovian dynamics. Later in Chap. ., we will present a new derivation of the FP description using a Markovian embedding technique [.,.,.,.,.,.]. To better understand the technical and conceptual difference of our approach, we will here also review some earlier work, in particular, Refs. [.,.,.].
extinguish
发表于 2025-3-25 22:25:57
Approximation for the Two-time Probability density the Fokker-Planck hierarchy. In particular, we have discussed the perturbation theory and the force-linearization closure (Chap. .). While these approaches render quite accurate descriptions of the intrawell dynamics, they do not yield any information about the .-time PDF.
infatuation
发表于 2025-3-26 01:35:46
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皮萨
发表于 2025-3-26 07:13:21
Summaryis a colloidal (Brownian) particle subject to a position-dependent, time-delayed feedback force and nonlinear static forces stemming from a potential. We describe its noisy motion by a Langevin equation, which is, due to the delay, non-local in time and infinite-dimensional.
Inelasticity
发表于 2025-3-26 11:55:10
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想象
发表于 2025-3-26 16:41:51
Force-Linearization ClosureIn this chapter, we turn to the problem of finding (approximate) probabilistic solutions of systems with delay. In particular, we discuss an approximation scheme for the steady-state one-time PDF, which we have introduced in Ref. [.], called . (FLC).
Interregnum
发表于 2025-3-26 19:04:16
Outlook—Open Questions and Further PerspectivesWe close with some comments putting the findings presented in this thesis into a broader perspective and giving an outlook on future research. We begin with formulating a few obvious follow-up questions and take a wider view towards the end.