Describing the state of a stochastic process
Abstract
The conventional way of mathematically describing the state of a classical stochastic process is criticized. A different approach, which emphasizes the important role of conditioning, is recommended.
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The conditional transition probability of a non-Markovian process depends on the initial probability vector.
“On the contrary, the conditional transition probability of a non-Markovian process does depend on the initial probability vector [27].”
From Markovianity and non-Markovianity in quantum and classical systems (2011) · cites this paper as [27]
For a non-Markovian process, a matrix Λ(t,s) satisfying Eq. (9) may exist, but it is not the conditional transition probability of the process.
“Indeed, for a given process one might find a matrix Λ ( t, s ) satisfying Eq. (9) even if the process is non-Markovian, however in this case the matrix is not the conditional transition probability of the process [27, 28].”
From Markovianity and non-Markovianity in quantum and classical systems (2011) · cites this paper as [27]
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Markovianity and non-Markovianity in quantum and classical systems
Vacchini, B., Smirne, A., Laine, E.-M., Piilo, J., & Breuer, H.-P. (2011) · New Journal of Physics · doi:10.1088/1367-2630/13/9/093004 · Cited by 198 · see citing works
A classical appraisal of quantum definitions of non-Markovian dynamics
Vacchini, B. (2012) · Journal of Physics B Atomic Molecular and Optical Physics · doi:10.1088/0953-4075/45/15/154007 · Cited by 52 · see citing works
Modeling quantum measurement probability as a classical stochastic process
Gillespie, D. T., Alltop, W. O., & Martin, J. M. (2001) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.1378791 · Cited by 3 · see citing works
Self-citationGillespie, D. T., Alltop, W. O., & Martin, J. M. (1999) · American Journal of Physics · doi:10.1119/1.19235 · Cited by 1 · see citing works
Self-citationVacchini, B. (2024) · Graduate texts in physics · doi:10.1007/978-3-031-58218-9_7
Stochastic Models of –1 Programmed Ribosomal Frameshifting
Bailey, B. L. (2014) · UA Campus Repository (The University of Arizona)
- Authors
- Gillespie, D. T.
- Affiliations
- Computational Sciences Branch (4B4000D), Naval Air Warfare Center, China Lake, California 93555
- Corresponding author
- Gillespie, Daniel T.
- ORCID
- Gillespie, Daniel T.
- Venue
- American Journal of Physics
- Published
- 1998-06-01
- Volume
- 66
- Issue
- 6
- Pages
- 533-536
- ISSN
- 0002-9505 (ISSN-L)
- 1943-2909
- OpenAlex
- W2059400565
- Cited by
- 6
- References
- 0
- Citations by year
- 2024: 1 · 2014: 1 · 2012: 1
- FWCI
- 0.95
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- American Journal of Physics (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Keywords
- stochastic processes, state description, conditioning, probability theory, classical stochastic processes
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