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Remarks on Non-Markov Processes
Open accessAbstract
It is emphasized that non-Markovian processes, which occur for instance in the case of colored noise, cannot be considered merely as corrections to the class of Markov processes but require special treatment. Many familiar concepts, such as first-passage times, no longer apply and need be reconsidered. Several methods of dealing with non-Markov processes are discussed. As an example a recent application to the transport of ions through a membrane is briefly mentioned.
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“Note that we are here only considering the one-point probabilities p ( t ), which are certainly not enough to assess Markovianity or non-Markovianity of a process according to the mathematically precise definition used in classical probability theory.”
From Markovianity and non-Markovianity in quantum and classical systems (2011) · cites this paper as [26]
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Cites
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Shuler, K. E. (1969) · CERN Document Server (European Organization for Nuclear Research) · Cited by 272
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Chen, X., & Silbey, R. J. (2011) · The Journal of Physical Chemistry B · doi:10.1021/jp111068w · Cited by 48
Metadata
- Authors
- van Kampen, N. G.
- Venue
- Brazilian Journal of Physics
- Publisher
- FapUNIFESP (SciELO)
- Published
- 1998-06
- Volume
- 28
- Issue
- 2
- ISSN
- 0103-9733 (ISSN-L)
- OpenAlex
- W2140826184
- Cited by
- 114
- References
- 2
- Citations by year
- 2026: 1 · 2025: 10 · 2024: 10 · 2023: 3 · 2022: 7 · 2021: 12 · 2020: 15 · 2019: 13 · 2018: 8 · 2017: 5 · 2016: 5 · 2015: 6 · 2014: 2 · 2013: 2 · 2012: 3
- FWCI
- 0.00
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- cc-by-nc
- Locations
- Brazilian Journal of Physics (publishedVersion, cc-by-nc)
- LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) (publishedVersion, other-oa)
- Americanae (AECID Library) (submittedVersion, other-oa)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › stochastic dynamics and bifurcation
- Physical Sciences › Mathematics › Mathematical Physics › Stochastic processes and statistical mechanics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Keywords
- non-Markovian processes, colored noise, first passage time, Markov processes, ion transport, membrane transport, stochastic processes
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