Dynamical Theories of Brownian Motion

Probability density functions for the translational itinerant oscillator

Coffey, W. T., & Evans, M. W. (1978) · Molecular Physics · doi:10.1080/00268977800100721 · Cited by 19

Investigating Training Objectives for Generative Speech Enhancement

Richter, J., de Oliveira, D., & Gerkmann, T. (2025) · IEEE International Conference on Acoustics Speech and Signal Processing · doi:10.1109/icassp49660.2025.10887784 · Cited by 25

Reciprocal Class of Jump Processes

Conforti, G., Pra, P. D., & Rœlly, S. (2015) · Journal of Theoretical Probability · doi:10.1007/s10959-015-0655-3 · Cited by 18

On extremals of the entropy production by ‘Langevin–Kramers’ dynamics

Muratore-Ginanneschi, P. (2014) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2014/05/p05013 · Cited by 18

Stochastic Description of a Bose–Einstein Condensate

Morato, L. M., & Ugolini, S. (2011) · Annales Henri Poincaré · doi:10.1007/s00023-011-0116-1 · Cited by 18

A smooth 3D model for fiber lay-down in nonwoven production processes

Klar, A., F. M., Maringer, J., et al. (2012) · Kinetic and Related Models · doi:10.3934/krm.2012.5.97 · Cited by 18

Rescuing Robert Brown—The Origins of Angio-Ovuly in Seed Cones of Conifers

TOMLINSON, P. B. (2012) · The Botanical Review · doi:10.1007/s12229-012-9104-5 · Cited by 18

Diffuse volume transport in fluids

Brenner, H. (2010) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2010.06.010 · Cited by 18

Homogenisation on homogeneous spaces

Li, X.-M. (2018) · Journal of the Mathematical Society of Japan · doi:10.2969/jmsj/07027546 · Cited by 18

Stochastic processes in conformal Riemann-Cartan-Weyl gravitation

Rapoport-Campodónico, D. L. (1991) · International Journal of Theoretical Physics · doi:10.1007/bf00675614 · Cited by 17

Random contractors with random nonlinear majorant functions

Lee, A. C. H., & Padgett, W. J. (1979) · Nonlinear Analysis · doi:10.1016/0362-546x(79)90098-1 · Cited by 18

Dynamical Measurements in the View of the Group Operators Theory

Shestakov, A. L., Sviridyuk, G. A., & Khudyakov, Y. V. (2014) · Springer proceedings in mathematics & statistics · doi:10.1007/978-3-319-12145-1_17 · Cited by 17

Influence of Magnetic Field on the Brownian Motion of Charged Particle

Furuse, H. (1970) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.28.559 · Cited by 17

Low‐gravity combustion synthesis: Theoretical analysis of experimental evidences

Locci, A. M., Licheri, R., Orrù, R., et al. (2006) · AIChE Journal · doi:10.1002/aic.11006 · Cited by 17

Extensions of positive definite integral kernels on the Heisenberg group

Jørgensen, P. E. T. (1990) · Journal of Functional Analysis · doi:10.1016/0022-1236(90)90060-x · Cited by 17

Phoresis in fluids

Brenner, H. (2011) · Physical Review E · doi:10.1103/physreve.84.066317 · Cited by 17

Perturbations of noise: Origins of isothermal flows

Garbaczewski, P. (1999) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.59.1498 · Cited by 16

Stochastic Control: A Function Space Approach

Balakrishnan, A. V. (1972) · SIAM Journal on Control · doi:10.1137/0310022 · Cited by 17

Physical significance of the Nelson-Newton laws

Garbaczewski, P. (1993) · Physics Letters A · doi:10.1016/0375-9601(93)91009-t · Cited by 17

Applications of the Fourier-Wiener transform to differential equations on infinite-dimensional spaces. I

Lee, Y. J. (1980) · Transactions of the American Mathematical Society · doi:10.1090/s0002-9947-1980-0583855-1 · Cited by 17

Burgers' flows as Markovian diffusion processes

Garbaczewski, P., Kondrat, G., & Olkiewicz, R. (1997) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.55.1401 · Cited by 17

Boson stochastic calculus

Parthasarathy, K. R. (1985) · Pramana · doi:10.1007/bf02846771 · Cited by 17

A Martingale Approach to Linear Recursive State Estimation

Balakrishnan, A. V. (1972) · SIAM Journal on Control · doi:10.1137/0310056 · Cited by 17

Quantum-like approach to the transversal and longitudinal beam dynamics: The halo problem

Khan, S. A., & Pusterla, M. (2000) · CERN Document Server (European Organization for Nuclear Research) · Cited by 16

Optomechanical generation of a photonic Bose-Einstein condensate

Weitz, M., Klaers, J., & Vewinger, F. (2013) · Physical Review A · doi:10.1103/physreva.88.045601 · Cited by 16

Microscopic chaos and Gaussian diffusion processes

Chew, L. Y., & Ting, C. H. A. (2002) · Physica A Statistical Mechanics and its Applications · doi:10.1016/s0378-4371(01)00613-6 · Cited by 16

The geometric phase and the spin-statistics relation

Bandyopadhyay, P. (2010) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.2010.0042 · Cited by 16

Efficient protocols for Stirling heat engines at the micro-scale

Muratore-Ginanneschi, P., & Schwieger, K. (2015) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/112/20002 · Cited by 16

Quantum mechanics can be formulated as a non-Markovian stochastic process

Skorobogatov, G. A., & Svertilov, S. I. (1998) · Physical Review A · doi:10.1103/physreva.58.3426 · Cited by 16

Equilibrium description of a particle system in a heat bath

Hernández, D. B., & Pavon, M. (1989) · Acta Applicandae Mathematicae · doi:10.1007/bf01307215 · Cited by 16

Dissipative forces and the algebra of operators in stochastic quantum mechanics

Lemos, N. A. (1980) · Physics Letters A · doi:10.1016/0375-9601(80)90080-8 · Cited by 15

The lagrangian approach to stochastic variational principles on curved manifolds

Aldrovandi, E., Dohrn, D., & Guerra, F. (1992) · Acta Applicandae Mathematicae · doi:10.1007/bf00047204 · Cited by 16

Mixtures in nonstable Lévy processes

Petroni, N. C. (2007) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/40/10/001 · Cited by 16

Quantized space-time and consequences

Namsrai, K. (1985) · International Journal of Theoretical Physics · doi:10.1007/bf00670326 · Cited by 16

Nelson-brown motion: Some question marks

Mielnik, B., & Tengstrand, G. (1980) · International Journal of Theoretical Physics · doi:10.1007/bf00670679 · Cited by 16

The motion of a large particle

Holley, R. A. (1969) · Transactions of the American Mathematical Society · doi:10.1090/s0002-9947-1969-0251796-0 · Cited by 16

Book Review: Le mouvement brownien relativiste

NELSON, E. B. (1978) · Bulletin of the American Mathematical Society · doi:10.1090/s0002-9904-1978-14432-2 · Cited by 16

Moderate maximal inequalities for the Ornstein-Uhlenbeck process

Jia, C., & Zhao, G. (2019) · Proceedings of the American Mathematical Society · doi:10.1090/proc/14804 · Cited by 15

Time reversal of diffusion processes under a finite entropy condition

Cattiaux, P., Conforti, G., Ivan Gentil, C., & Léonard, C. (2023) · Annales de l Institut Henri Poincaré Probabilités et Statistiques · doi:10.1214/22-aihp1320 · Cited by 15

Rigidity for Markovian maximal couplings of elliptic diffusions

Banerjee, S., & Kendall, W. S. (2016) · Probability Theory and Related Fields · doi:10.1007/s00440-016-0706-4 · Cited by 15

A Fubini theorem on a function space and its applications

Chung, H. S., Choi, J. G., & Chang, S. J. (2013) · Banach Journal of Mathematical Analysis · doi:10.15352/bjma/1358864557 · Cited by 15

Quaternion Algebra on 4D Superfluid Quantum Space-Time: Gravitomagnetism

Sbitnev, V. I. (2019) · Foundations of Physics · doi:10.1007/s10701-019-00236-4 · Cited by 15

Reconstruction of Observation from Distorted Data for the Optimal Dynamic Measurement Problem

Sagadeeva, M. A. (2019) · Bulletin of the South Ural State University Series Mathematical Modelling Programming and Computer Software · doi:10.14529/mmp190207 · Cited by 15

The Differential Entropy of Mixtures: New Bounds and Applications

Melbourne, J., Talukdar, S., Bhaban, S., et al. (2022) · IEEE Transactions on Information Theory · doi:10.1109/tit.2022.3140661 · Cited by 15

Stochastic Mathematical Model of Internal Waves

Богомолов, А. В., Bychkov, Е. V., & Kotlovanov, K. Y. (2020) · Bulletin of the South Ural State University Series Mathematical Modelling Programming and Computer Software · doi:10.14529/mmp200203 · Cited by 15

State-dependent graviton noise in the equation of geodesic deviation

Haba, Z. (2021) · The European Physical Journal C · doi:10.1140/epjc/s10052-020-08805-y · Cited by 15

From Second-Order Differential Geometry to Stochastic Geometric Mechanics

Huang, Q., & Zambrini, J.-C. (2023) · Journal of Nonlinear Science · doi:10.1007/s00332-023-09917-x · Cited by 15

On the stochastic mechanics of the free relativistic particle

Pavon, M. (2001) · Journal of Mathematical Physics · doi:10.1063/1.1401135 · Cited by 15

Brownian Dynamics of Particles “Dressed” by Chiral Director Configurations in Lyotropic Chromonic Liquid Crystals

Martinez, A., Collings, P. J., & Yodh, A. G. (2018) · Physical Review Letters · doi:10.1103/physrevlett.121.177801 · Cited by 15

Intrinsic bounds on some real-valued stationary random functions

Borell, C. (1985) · Lecture notes in mathematics · doi:10.1007/bfb0074946 · Cited by 15

Test of some fundamental principles in physics via quantum interference with neutrons and photons

Camacho, A., & Camacho-Galván, A. (2007) · Reports on Progress in Physics · doi:10.1088/0034-4885/70/11/r04 · Cited by 18

The Green–Kubo formula, autocorrelation function and fluctuation spectrum for finite Markov chains with continuous time

Chen, Y., Chen, X., & Qian, M. (2006) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/39/11/001 · Cited by 15

Three months journeying of a Hawaiian monk seal

Brillinger, D. R., Stewart, B. S., & Littnan, C. L. (2008) · Institute of Mathematical Statistics eBooks · doi:10.1214/193940307000000473 · Cited by 15

Quantum decay process of metastable vacuum states in SU(2) Yang-Mills theory: A probability theoretical point of view

Yasue, K. (1978) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.18.532 · Cited by 15

Enhancing Least Squares Monte Carlo with diffusion bridges: an application to energy facilities

Pellegrino, T., & Sabino, P. (2014) · Quantitative Finance · doi:10.1080/14697688.2014.941913 · Cited by 14

Energy representation for nonequilibrium Brownian-like systems: Steady states and fluctuation relations

Lev, B. I., & Kiselev, A. D. (2010) · Physical Review E · doi:10.1103/physreve.82.031101 · Cited by 14

Electron vortex beams in a magnetic field and spin filter

Chowdhury, D., Basu, B., & Bandyopadhyay, P. (2015) · Physical Review A · doi:10.1103/physreva.91.033812 · Cited by 14

Some basic relationships among transforms, convolution products, first variations and inverse transforms

Chang, S. J., Chung, H., & Skoug, D. (2012) · Open Mathematics · doi:10.2478/s11533-012-0148-x · Cited by 14

On the solvability of nonautonomous stochastic differential equations with current velocities

Azarina, S. V., & Gliklikh, Y. E. (2016) · Mathematical Notes · doi:10.1134/s0001434616070014 · Cited by 14

Quaternion Algebra on 4D Superfluid Quantum Space-Time: Can Dark Matter Be a Manifestation of the Superfluid Ether?

Sbitnev, V. I. (2021) · Universe · doi:10.3390/universe7020032 · Cited by 14

Dynamical Systems in the Variational Formulation of the Fokker—Planck Equation by the Wasserstein Metric

Mikami, T. (2000) · Applied Mathematics & Optimization · doi:10.1007/s002450010008 · Cited by 14

On time-reversal and space-time harmonic processes for Markovian quantum channels

Ticozzi, F., & Pavon, M. (2010) · Quantum Information Processing · doi:10.1007/s11128-010-0186-x · Cited by 13

Overdamped langevin dynamics simulations of grain boundary motion

Baruffi, C., Finel, A., Bouar, Y. L., et al. (2019) · Materials Theory · doi:10.1186/s41313-019-0016-1 · Cited by 14

Bouncing Oil Droplets, de Broglie’s Quantum Thermostat, and Convergence to Equilibrium

Hatifi, M., Willox, R., Colin, S., & Durt, T. (2018) · Entropy · doi:10.3390/e20100780 · Cited by 18

Transience and Non-explosion of Certain Stochastic Newtonian Systems

Kolokoltsov, V. N., Schilling, R. L., & Tyukov, A. (2002) · Electronic Journal of Probability · doi:10.1214/ejp.v7-118 · Cited by 14

Estimates for the maximal operator of the Ornstein-Uhlenbeck semigroup

Gutiérrez, C. E., & R., W. O. U. (1991) · Proceedings of the American Mathematical Society · doi:10.1090/s0002-9939-1991-1068123-9 · Cited by 14

Time reversal of diffusion processes

Haussmann, U. G., & Pardoux, É. (2005) · Springer eBooks · doi:10.1007/bfb0005072 · Cited by 14

A molecular approach to the foundations of the theory of solute transport in porous media

Gupta, V. K., Bhattacharya, R., & Sposito, G. (1981) · Journal of Hydrology · doi:10.1016/0022-1694(81)90078-0 · Cited by 14

A discrete geometry: Speculations on a new framework for classical electrodynamics

Hemion, G. (1988) · International Journal of Theoretical Physics · doi:10.1007/bf00670680 · Cited by 14

Quelques resultats de «mecanique stochastique»

Zheng, W., & Meyer, P. A. (1984) · Lecture notes in mathematics · doi:10.1007/bfb0100047 · Cited by 14

A model for the frequency dependence of the polarizability of a polar molecule

Calderwood, J. H., Coffey, W. T., Morita, A., et al. (1976) · Proceedings of the Royal Society of London A Mathematical and Physical Sciences · doi:10.1098/rspa.1976.0174 · Cited by 14

Markov Marginal Problems and Their Applications to Markov Optimal Control

Mikami, T. (1999) · Birkhäuser Boston eBooks · doi:10.1007/978-1-4612-1784-8_27 · Cited by 13

Biophysics of Consciousness: A Scale-Invariant Acoustic Information Code of a Superfluid Quantum Space Guides the Mental Attribute of the Universe

Meijer, D. K. F., Jerman, I., Melkikh, A. V., & Sbitnev, V. I. (2020) · Studies in Rhythm Engineering · doi:10.1007/978-981-15-7253-1_8 · Cited by 17

Ionization and high harmonic generation of two-dimensional quasiperiodic structures in arbitrarily polarized strong laser fields

Li, L., & He, F. (2016) · Journal of the Optical Society of America B · doi:10.1364/josab.34.000052 · Cited by 13

Homogenization for a Class of Generalized Langevin Equations with an Application to Thermophoresis

Lim, S. H., & Wehr, J. (2018) · Journal of Statistical Physics · doi:10.1007/s10955-018-2192-9 · Cited by 13

Connecting Two Stochastic Theories That Lead to Quantum Mechanics

de la Peña, L., Cetto, A. M., & Valdés-Hernández, A. (2020) · Frontiers in Physics · doi:10.3389/fphy.2020.00162 · Cited by 13

Information in asset pricing: a wave function approach

Ishio, H., & Haven, E. E. (2009) · Annalen der Physik · doi:10.1002/andp.200810333 · Cited by 13

A CLASSICAL MECHANICAL MODEL OF BROWNIAN MOTION WITH PLURAL PARTICLES

Kusuoka, S., & Song, L. (2010) · Reviews in Mathematical Physics · doi:10.1142/s0129055x10004077 · Cited by 13

Firm's default ? new methodological approach and preliminary evidence from Poland

Berent, T. S., Bławat, B., Dietl, M., et al. (2017) · Equilibrium Quarterly Journal of Economics and Economic Policy · doi:10.24136/eq.v12i4.39 · Cited by 13

Elliptic stochastic quantization

Albeverio, S. A., Vecchi, F. C. D., & Gubinelli, M. (2020) · The Annals of Probability · doi:10.1214/19-aop1404 · Cited by 21

Homogenization for Generalized Langevin Equations with Applications to Anomalous Diffusion

Lim, S. H., Wehr, J., & Lewenstein, M. (2020) · Annales Henri Poincaré · doi:10.1007/s00023-020-00889-2 · Cited by 13

Quantified overdamped limit for kinetic Vlasov–Fokker–Planck equations with singular interaction forces

Choi, Y.-P., & Tse, O. T. C. (2022) · Journal of Differential Equations · doi:10.1016/j.jde.2022.05.008 · Cited by 13

Stochastic quantization on Lorentzian manifolds

Kuipers, F. (2021) · Journal of High Energy Physics · doi:10.1007/jhep05(2021)028 · Cited by 13

Non-Markovian effects on the Brownian motion of a free particle

Bolivar, A. O. (2011) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2011.04.014 · Cited by 13

Stochastic-hydrodynamic model of halo formation in charged particle beams

Petroni, N. C., Martino, S. D., Siena, S. D., et al. (2003) · Physical Review Special Topics - Accelerators and Beams · doi:10.1103/physrevstab.6.034206 · Cited by 13

The generalized F�nyes-Nelson model for free scalar field theory

Davidson, M. P. (1980) · Letters in Mathematical Physics · doi:10.1007/bf00417501 · Cited by 13

Global existence for the Vlasov‐Poisson/Fokker‐Planck equation in many dimensions, for small data

Triolo, L. (1988) · Mathematical Methods in the Applied Sciences · doi:10.1002/mma.1670100412 · Cited by 13

From stochastic processes to the hydrodynamic equations

Beck, C. H., & Roepstorff, G. (1990) · Physica A Statistical Mechanics and its Applications · doi:10.1016/0378-4371(90)90195-x · Cited by 13

Stochastic quantization of the vector-meson field

Siena, S. D., Guerra, F., & Ruggiero, P. (1983) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.27.2912 · Cited by 13

On the statistical origins of the de Broglie-Bohm quantum potential: Brownian motion in a field of force as Bernstein diffusion

Garbaczewski, P. (1993) · Physics Letters A · doi:10.1016/0375-9601(93)90718-f · Cited by 13

Quantum fluctuations — An introduction

NELSON, E. B. (1984) · Physica A Statistical Mechanics and its Applications · doi:10.1016/0378-4371(84)90266-8 · Cited by 13

Stochastic mechanics and quantum interference

Petroni, N. C. (1989) · Physics Letters A · doi:10.1016/0375-9601(89)90851-7 · Cited by 13

SOME UNSOLVED PROBLEMS IN QUANTUM LOGICS

Gudder, S. (1978) · Elsevier eBooks · doi:10.1016/b978-0-12-473250-6.50010-8 · Cited by 13

The origin of the algebra of quantum operators in the stochastic formulation of quantum mechanics

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Molecular rototranslation in condensed phases : Single particle theory

Evans, M. W., & Grigolini, P. (1980) · Molecular Physics · doi:10.1080/00268978000101141 · Cited by 13

Probabilistic causality in quantum mechanics

Suppes, P. (1990) · Journal of Statistical Planning and Inference · doi:10.1016/0378-3758(90)90078-9 · Cited by 11

Exploiting thermal noise for an efficient actomyosin sliding mechanism

Buonocore, A., & Ricciardi, L. M. (2003) · Mathematical Biosciences · doi:10.1016/s0025-5564(02)00217-1 · Cited by 13

Weak Solutions for the Compressible Navier-Stokes Equations with Density Dependent Viscosities

Bresch, D., & Desjardins, B. (2018) · Springer eBooks · doi:10.1007/978-3-319-13344-7_44 · Cited by 12

Spectrum of Schrödinger Hamiltonian operator with singular inverted complex and Kratzer’s molecular potentials in fractional dimensions

El‐Nabulsi, R. A. (2018) · The European Physical Journal Plus · doi:10.1140/epjp/i2018-12149-0 · Cited by 12

Towards Measuring the Maxwell–Boltzmann Distribution of a Single Heated Particle

Su, X., Fischer, A., & Cichos, F. (2021) · Frontiers in Physics · doi:10.3389/fphy.2021.669459 · Cited by 12

ИСПОЛЬЗОВAНИЕ ПОТЕНЦИAЛA СОЦИAЛЬНЫХ ПAРТНЕРОВ В ПОДГОТОВКЕ БУДУЩИХ ПЕДAГОГОВ

Атабекова, Б. Б. (2024) · Habaršy. Pedagogika ġylymdary seriâsy · doi:10.51889/2959-5762.2023.80.4.019

Prim�rzerlegung in Steinschen Algebren

Förster, O. (1964) · Mathematische Annalen · doi:10.1007/bf01362567 · Cited by 32

�ber unirationale Scharen auf algebraischen Mannigfaltigkeiten

Reich, L. (1966) · Mathematische Annalen · doi:10.1007/bf01364537 · Cited by 4

Produkttreue Klassen universeller Algebren

Timm, J. (1969) · Archiv der Mathematik · doi:10.1007/bf01899454 · Cited by 1

Approximation of fixed points of multifunctions in partial metric spaces

Paesano, D. (2015) · Hacettepe Journal of Mathematics and Statistics · doi:10.15672/hjms.2015449088