The DOI matches its Crossref record.
Dynamical Theories of Brownian Motion
Overview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“In view of the similarity between Bohmian mechanics and stochastic mechanics [44,45,46], for which similarity see [35,28], all of our arguments and results can be transferred to stochastic mechanics without significant modification.”
From Quantum equilibrium and the origin of absolute uncertainty (1992) · cites this paper as [45]
Citations
Cited by
Sorted by citations
Items 501–600 of 1,000
Favini, A., Загребина, С. А., & Sviridyuk, G. A. (2022) · Mediterranean Journal of Mathematics · doi:10.1007/s00009-021-01940-0 · Cited by 8
Stability of hybrid pantograph stochastic functional differential equations
Wu, H., Hu, J., & Yuan, C. (2021) · Systems & Control Letters · doi:10.1016/j.sysconle.2021.105105 · Cited by 8
Bohm's Metaphors, Causality, and the Quantum Potential
Guarini, M. (2003) · Erkenntnis · doi:10.1023/a:1023941005266 · Cited by 8
Solvable Models of Resonances and Decays
Exner, P. (2013) · Operator theory · doi:10.1007/978-3-0348-0591-9_3 · Cited by 8
Renormalization group and instantons in stochastic nonlinear dynamics
Volchenkov, D. (2009) · The European Physical Journal Special Topics · doi:10.1140/epjst/e2009-01001-3 · Cited by 8
Petroni, N. C. (2011) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/44/16/165305 · Cited by 8
Optimal stochastic transport in inhomogeneous thermal environments
Bo, S., Aurell, E. M., Eichhorn, R., et al. (2013) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/103/10010 · Cited by 8
Bernstein Diffusions for a Class of Linear Parabolic Partial Differential Equations
Vuillermot, P.-A., & Zambrini, J.-C. (2012) · Journal of Theoretical Probability · doi:10.1007/s10959-012-0426-3 · Cited by 8
The principles of a stochastic formulation of quantum theory
Kyprianidis, A. (1992) · Foundations of Physics · doi:10.1007/bf01883734 · Cited by 8
Operators versus functions: from quantum dynamical semigroups to tomographic semigroups
Aniello, P. (2013) · Journal of Physics Conference Series · doi:10.1088/1742-6596/474/1/012005 · Cited by 8
On The Local Times of Fractional Ornstein–Uhlenbeck Process
Yan, L., & Tian, M. (2005) · Letters in Mathematical Physics · doi:10.1007/s11005-005-0018-6 · Cited by 8
Couplings, gradient estimates and logarithmic Sobolev inequalitiy for Langevin bridges
Conforti, G., & von Renesse, M. (2017) · Probability Theory and Related Fields · doi:10.1007/s00440-017-0814-9 · Cited by 8
The 2005 Neyman Lecture: Dynamic Indeterminism in Science
Brillinger, D. R. (2008) · Statistical Science · doi:10.1214/07-sts246 · Cited by 8
Velocity auto correlation function of a confined Brownian particle
Noushad, A., Shajahan, S., & Sahoo, M. (2021) · The European Physical Journal B · doi:10.1140/epjb/s10051-021-00217-5 · Cited by 8
Parabolic Equations Associated with the Number Operator
Piech, M. A. (1974) · Transactions of the American Mathematical Society · doi:10.2307/1996802 · Cited by 8
Introduction to Nelson Stochastic Mechanics as a Model for Quantum Mechanics
Guerra, F. (1995) · Springer eBooks · doi:10.1007/978-94-011-0029-8_28 · Cited by 9
Processus de diffusion gouverne par la forme de dirichlet de l'operateur de Schrödinger
Carmona, R. A. (1979) · Lecture notes in mathematics · doi:10.1007/bfb0070893 · Cited by 8
Schrödinger uncertainty relation for a quantum oscillator in a thermostat
Sukhanov, A. D. (2006) · Theoretical and Mathematical Physics · doi:10.1007/s11232-006-0106-5 · Cited by 8
On the theory of generalized diffusion processes in many-particle systems
Altenberger, A. R. (1978) · Physica A Statistical Mechanics and its Applications · doi:10.1016/0378-4371(78)90139-5 · Cited by 8
Ginovska, M., Czechowski, G., Déjardin, J., et al. (2005) · Liquid Crystals · doi:10.1080/02678290500116946 · Cited by 8
Hennion, H. (1973) · Probability Theory and Related Fields · doi:10.1007/bf00533100 · Cited by 8
Albeverio, S. A., & Høegh-Krohn, R. J. (1981) · Lecture notes in mathematics · doi:10.1007/bfb0088741 · Cited by 8
Frictionless random dynamics: hydrodynamical formalism
Czopnik, R., & Garbaczewski, P. (2002) · Physica A Statistical Mechanics and its Applications · doi:10.1016/s0378-4371(02)01343-2 · Cited by 8
Lévy–Student processes for a stochastic model of beam halos
Petroni, N. C., Martino, S. D., Siena, S. D., et al. (2006) · Nuclear Instruments and Methods in Physics Research Section A Accelerators Spectrometers Detectors and Associated Equipment · doi:10.1016/j.nima.2006.01.011 · Cited by 8
Sz�sz, D. (1980) · Journal of Statistical Physics · doi:10.1007/bf01012593 · Cited by 8
Stochastic mechanics of spin-½ particles
Guerra, F., & Marra, R. (1984) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.30.2579 · Cited by 8
Truman, A., & Williams, D. S. (1990) · Birkhäuser Boston eBooks · doi:10.1007/978-1-4684-0564-4_8 · Cited by 8
A new interpretation of the Schrödinger equation, and its extension to dissipative phenomena
Fronteau, J., & Tellez-Arenas, A. (1976) · Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B · doi:10.1007/bf02749423 · Cited by 8
Thermal mechanics: A quantum mechanical analogue of nonequilibrium statistical thermodynamics
Zambrini, J.-C., & Yasue, K. (1980) · Annals of Physics · doi:10.1016/0003-4916(80)90123-2 · Cited by 8
Lim, S. (1983) · Letters in Mathematical Physics · doi:10.1007/bf00402246 · Cited by 8
Conditioning in quantum mechanics
Petroni, N. C. (1991) · Physics Letters A · doi:10.1016/0375-9601(91)90597-2 · Cited by 8
Суханов, А. Д. (2002) · Теоретическая и математическая физика · doi:10.4213/tmf373 · Cited by 8
Ivanova, B. B., & Spiteller, M. (2018) · Journal of Molecular Structure · doi:10.1016/j.molstruc.2018.07.055 · Cited by 7
Adaptive Dynamics Simulation of Interference Phenomenon for Physical and Biological Systems
Ando, T., Asano, M., Khrennikov, A. Y., et al. (2023) · Entropy · doi:10.3390/e25111487 · Cited by 7
Ergodicity of the underdamped mean-field Langevin dynamics
Kazeykina, A., Ren, Z., Tan, X., et al. (2024) · The Annals of Applied Probability · doi:10.1214/23-aap2036 · Cited by 7
Structure Process, Weak Values and Local Momentum
Hiley, B. J. (2016) · Journal of Physics Conference Series · doi:10.1088/1742-6596/701/1/012010 · Cited by 7
Hydrodynamics of superfluid quantum space: particle of spin-1/2 in a magnetic field
Sbitnev, V. I. (2017) · Quantum Studies Mathematics and Foundations · doi:10.1007/s40509-017-0119-9 · Cited by 7
Carmele, A., Parkins, A. S., & Knorr, A. (2020) · Physical Review A · doi:10.1103/physreva.102.033712 · Cited by 7
An entropic interpolation problem for incompressible viscous fluids
Arnaudon, M., Cruzeiro, A. B., Léonard, C., et al. (2020) · Annales de l Institut Henri Poincaré Probabilités et Statistiques · doi:10.1214/19-aihp1036 · Cited by 7
Stochastic optimal transport revisited
Mikami, T. (2021) · Partial Differential Equations and Applications · doi:10.1007/s42985-020-00059-3 · Cited by 7
A Berry–Esseen Bound in the Smoluchowski–Kramers Approximation
Tan, N. V., & Dũng, N. T. (2020) · Journal of Statistical Physics · doi:10.1007/s10955-020-02564-6 · Cited by 7
Local Invertibility of Adapted Shifts on Wiener Space and Related Topics
Lassalle, R., & Üstünel, A. S. (2013) · Springer proceedings in mathematics & statistics · doi:10.1007/978-1-4614-5906-4_3 · Cited by 7
Non-Newtonian fluids and stochastic analysis on the groups of diffeomorphisms
Gliklikh, Y. E., & Zalygaeva, M. E. (2014) · Applicable Analysis · doi:10.1080/00036811.2014.918263 · Cited by 7
Lévy-Student distributions for halos in accelerator beams
Petroni, N. C., Martino, S. D., Siena, S. D., et al. (2005) · Physical Review E · doi:10.1103/physreve.72.066502 · Cited by 7
Self-contained framework of stochastic mechanics for reconstructing the Onsager-Machlup theory
Hasegawa, H. (1986) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.33.2508 · Cited by 7
Nonequilibrium Thermodynamics of the First and Second Kind: Averages and Fluctuations
Öttinger, H. C. (2010) · Journal of Statistical Physics · doi:10.1007/s10955-010-9919-6 · Cited by 7
On solvability of stochastic differential inclusions with current velocities
Gliklikh, Y. E., & Makarova, A. V. (2011) · Applicable Analysis · doi:10.1080/00036811.2011.579565 · Cited by 7
Noncommutative Geometry and Stochastic Processes
Frasca, M. (2017) · Lecture notes in computer science · doi:10.1007/978-3-319-68445-1_57 · Cited by 7
Extremal Curves in Wasserstein Space
Conforti, G., & Pavon, M. (2017) · Lecture notes in computer science · doi:10.1007/978-3-319-68445-1_11 · Cited by 7
Stochastic quantization of relativistic theories
Kuipers, F. (2021) · Sussex Research Online (University of Sussex) · Cited by 7
Stochastic mean-field dynamics for fermions in the weak-coupling limit
Denis Lacroix, A. (2006) · Physical Review C · doi:10.1103/physrevc.73.044311 · Cited by 8
The Smoluchowski limit for a simple mechanical model
Calderoni, P., & D�rr, D. (1989) · Journal of Statistical Physics · doi:10.1007/bf01041604 · Cited by 7
Stochastic derivation of the Klein-Gordon equation from classical relativistic action
Morato, L. M. (1991) · Physics Letters A · doi:10.1016/0375-9601(91)90027-6 · Cited by 7
Théorème de Noether stochastique
Cresson, J., & Darses, S. (2007) · Comptes Rendus Mathématique · doi:10.1016/j.crma.2006.12.017 · Cited by 7
Outline of a Nonlinear, Relativistic Quantum Mechanics of Extended Particles
Mielke, E. W. (1981) · Fortschritte der Physik · doi:10.1002/prop.19810291103 · Cited by 7
Stochastic derivation of the Birula-Mycielski nonlinear wave equation
Lemos, N. A. (1983) · Physics Letters A · doi:10.1016/0375-9601(83)90276-1 · Cited by 7
Garbaczewski, P. (1998) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.57.569 · Cited by 7
Equations de diffusion generales sur des reseaux infinis
Lumer, G. (1984) · Lecture notes in mathematics · doi:10.1007/bfb0099027 · Cited by 7
Les Processus Stochastiques de 1950 à Nos Jours
Meyer, P. A. (2000) · Birkhäuser Basel eBooks · doi:10.1007/978-3-0348-8968-1_27 · Cited by 7
Bernstein Polynomials and Brownian Motion
Kowalski, E. (2006) · American Mathematical Monthly · doi:10.2307/27642086 · Cited by 7
Roy, R. R. (2010) · Springer eBooks · doi:10.1007/978-1-4419-6050-4_3 · Cited by 7
Random Integrodifferential Equations
Kannan, D. (1978) · Elsevier eBooks · doi:10.1016/b978-0-12-095601-2.50008-0 · Cited by 7
Limit theorems in stochastic biochemical modeling
Del Grosso, G., & Marchetti, F. (1983) · Mathematical Biosciences · doi:10.1016/0025-5564(83)90086-x · Cited by 7
On the hidden supersymmetry in stochastic quantization
Noga, M. (1988) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.38.3158 · Cited by 7
Stochastic Incompleteness of Quantum Mechanics
Suppes, P., & Zanotti, M. (1976) · Springer eBooks · doi:10.1007/978-94-010-9466-5_15 · Cited by 7
The Schrödinger Equation — 50 Years Later
Barut, A. O. (1977) · Zeitschrift für Naturforschung A · doi:10.1515/zna-1977-3-427 · Cited by 7
Local and global Markoff fields
Albeverio, S. A., & Høegh-Krohn, R. J. (1984) · Reports on Mathematical Physics · doi:10.1016/0034-4877(84)90017-x · Cited by 7
Batanov-Gaukhman, M. (2024) · doi:10.24108/preprints-3113016 · Cited by 7
Helland, I. S. (2021) · Springer eBooks · doi:10.1007/978-3-030-81923-1_5 · Cited by 6
MODELING THE EFFECTS OF CHANNEL NOISE IN NEURONS: A STUDY BASED ON DISSIPATIVE STOCHASTIC MECHANICS
Güler, M. (2006) · Fluctuation and Noise Letters · doi:10.1142/s0219477506003239 · Cited by 6
A low-rank approach to the computation of path integrals
Litsarev, M. S., & Oseledets, I. V. (2015) · Journal of Computational Physics · doi:10.1016/j.jcp.2015.11.009 · Cited by 6
Suzuki, M., Kameda, T., Doi, A., et al. (2018) · doi:10.1117/12.2301383 · Cited by 6
Brownian Motion at the Speed of Light: A New Lorentz Invariant Family of Processes
Serva, M. (2021) · Journal of Statistical Physics · doi:10.1007/s10955-021-02734-0 · Cited by 6
Cresson, J., Laurent Nottale, A., & Lehner, T. (2021) · Journal of Mathematical Physics · doi:10.1063/5.0037265 · Cited by 6
3D-space and the preferred basis cannot uniquely emerge from the quantum structure
Stoica, O. C. (2022) · Advances in Theoretical and Mathematical Physics · doi:10.4310/atmp.2022.v26.n10.a12 · Cited by 26
A hybrid parareal Monte Carlo algorithm for parabolic problems
Dabaghi, J., Maday, Y., & Zoia, A. (2022) · Journal of Computational and Applied Mathematics · doi:10.1016/j.cam.2022.114800 · Cited by 6
Development of the Theory of Optimal Dynamic Measurements
Bychkov, Е. V., Загребина, С. А., Zamyshlyaeva, A. A., et al. (2022) · Bulletin of the South Ural State University Series Mathematical Modelling Programming and Computer Software · doi:10.14529/mmp220302 · Cited by 6
Relativistic Fermion and Boson Fields: Bose-Einstein Condensate as a Time Crystal
Sbitnev, V. I. (2023) · Symmetry · doi:10.3390/sym15020275 · Cited by 6
Extending the Regime of Linear Response with Synthetic Forcings
Spacek, R., & Stoltz, G. (2023) · Multiscale Modeling and Simulation · doi:10.1137/23m1557611 · Cited by 6
Quantum mechanics from stochastic processes
Kuipers, F. (2023) · The European Physical Journal Plus · doi:10.1140/epjp/s13360-023-04184-x · Cited by 6
A history of the relation between fluctuation and dissipation
Darrigol, O. (2023) · The European Physical Journal H · doi:10.1140/epjh/s13129-023-00058-z · Cited by 6
Cushing, J. T. (1992) · Springer eBooks · doi:10.1007/978-1-4615-3332-0_3 · Cited by 6
EXTRACTING ENERGY FROM NOISE: NOISE BENEFITS IN HYSTERETIC SYSTEMS
Dimian, M. (2008) · NANO · doi:10.1142/s1793292008001258 · Cited by 6
Numerical simulation of optically trapped particles
Volpe, G., & Volpe, G. (2014) · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · doi:10.1117/12.2070777 · Cited by 6
Local kinetic interpretation of entropy production through reversed diffusion
Porporato, A. M., Kramer, P. R., Cassiani, M., Daly, E., & Mattingly, J. C. (2011) · Physical Review E · doi:10.1103/physreve.84.041142 · Cited by 6
A universal envelope for Gaussian processes and their kernels
Jørgensen, P. E. T. (2013) · Journal of Applied Mathematics and Computing · doi:10.1007/s12190-013-0678-9 · Cited by 5
Phase Space Reduction of the One-Dimensional Fokker-Planck (Kramers) Equation
Kalinay, P., & Percus, J. K. (2012) · Journal of Statistical Physics · doi:10.1007/s10955-012-0570-2 · Cited by 6
Chafaï, D., & Malrieu, F. (2016) · Mathématiques et applications · doi:10.1007/978-3-662-49768-5 · Cited by 6
Entropy Chaos and Bose-Einstein Condensation
Albeverio, S. A., Vecchi, F. C. D., & Ugolini, S. (2017) · Journal of Statistical Physics · doi:10.1007/s10955-017-1820-0 · Cited by 6
О разрешимости неавтономных стохастических дифференциальных уравнений с текущими скоростями
Azarina, S. V., & Gliklikh, Y. E. (2016) · Математические заметки · doi:10.4213/mzm11130 · Cited by 6
Quaternion Algebra on 4D Superfluid Quantum Space-Time. Dirac’s Ghost Fermion Fields.
Sbitnev, V. I. (2022) · Foundations of Physics · doi:10.1007/s10701-021-00533-x · Cited by 6
Rough Homogenisation with Fractional Dynamics
Gehringer, J., & Li, X.-M. (2021) · Springer proceedings in mathematics & statistics · doi:10.1007/978-3-030-87432-2_8 · Cited by 6
On Existence of Solutions to Stochastic Differential Inclusions with Current Velocities II
Gliklikh, Y. E., & Makarova, A. V. (2016) · Journal of Computational and Engineering Mathematics · doi:10.14529/jcem160106 · Cited by 6
Yasue, K., Jibu, M., Misawa, T., & Zambrini, J.-C. (1988) · Annals of the Institute of Statistical Mathematics · doi:10.1007/bf00053954 · Cited by 6
Around the entropic Talagrand inequality
Conforti, G., & Ripani, L. (2020) · Bernoulli · doi:10.3150/19-bej1163 · Cited by 6
Stochastic incompleteness of quantum mechanics
Suppes, P., & Zanotti, M. (1974) · Synthese · doi:10.1007/bf00484963 · Cited by 6
Localization of Relative Entropy in Bose–Einstein Condensation of Trapped Interacting Bosons
Morato, L. M., & Ugolini, S. (2013) · Progress in probability · doi:10.1007/978-3-0348-0545-2_9 · Cited by 6
Brownian Motion and Potential Theory
Taylor, M. E. (2010) · Applied mathematical sciences · doi:10.1007/978-1-4419-7052-7_5 · Cited by 6
On stochastic Hamiltonian mechanics for diffusion processes
Misawa, T. (1986) · Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B · doi:10.1007/bf02722218 · Cited by 6
Critical Ornstein-Uhlenbeck processes
Pavon, M. (1986) · Applied Mathematics & Optimization · doi:10.1007/bf01442240 · Cited by 6
Metadata
- Authors
- Nelson, E.
- Corresponding author
- Nelson, Edward
- Venue
- Princeton University Press eBooks
- Publisher
- Princeton University Press
- Published
- 1967-12-31
- OpenAlex
- W4300023393
- Cited by
- 1,251
- References
- 0
- Citations by year
- 2026: 18 · 2025: 17 · 2024: 32 · 2023: 23 · 2022: 32 · 2021: 51 · 2020: 30 · 2019: 42 · 2018: 37 · 2017: 29 · 2016: 31 · 2015: 36 · 2014: 30 · 2013: 32 · 2012: 25
- FWCI
- 9.43
- Type
- book
- Language
- en
- Open access
- closed
- Locations
- Princeton University Press eBooks (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Statistical Mechanics and Entropy
- Physical Sciences › Mathematics › Mathematical Physics › Stochastic processes and statistical mechanics
- Keywords
- Brownian motion, dynamical theory, molecular motion, diffusion, kinetic theory of gases, statistical mechanics
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review