Dynamical Theories of Brownian Motion

Learning as Progressive Biasing of a Random Walk Process: Toward an Ecological Theory of Exploratory Learning

Effken, J., & Kadar, E. (2001) · Ecological Psychology · doi:10.1207/s15326969eco1301_1 · Cited by 6

MARKET FORCES AND DYNAMIC ASSET PRICING

Peškir, G., & Shorish, J. (2002) · Stochastic Analysis and Applications · doi:10.1081/sap-120014553 · Cited by 6

Quantum stochastic integration and quantum stochastic differential equations

Barnett, C., Goldstein, S., & Wilde, I. F. (1994) · Mathematical Proceedings of the Cambridge Philosophical Society · doi:10.1017/s0305004100072807 · Cited by 6

Girsanov transformation and two stochastic optimal control problems. The Schrödinger system and related controllability results

Blaquière, A. (2006) · Springer eBooks · doi:10.1007/bfb0041196 · Cited by 6

The interaction of propagating space-time fluctuations with wave packets

Power, W. L. (1999) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.1999.0346 · Cited by 5

The positive-temperature random electromagnetic field in classical stochastic electrodynamics

Moore, S. M. (1979) · Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimento · doi:10.1007/bf02725424 · Cited by 6

Natural processes and Doob-Meyer decompositions over a probability gage space

Barnett, C., & Wilde, I. F. (1984) · Journal of Functional Analysis · doi:10.1016/0022-1236(84)90046-6 · Cited by 6

The stochastic mechanics of the ground-state of the hydrogen atom

Truman, A., & Lewis, J. T. (1986) · Lecture notes in mathematics · doi:10.1007/bfb0080216 · Cited by 6

1 REMARKS ON OSMOSIS, QUANTUM MECHANICS, AND GRAVITYPreprint

Carroll, R. (2016) · Cited by 4

Quantum Potential and Random Phase - Space Dynamics

Czopnik, R., & Garbaczewski, P. (2002) · CERN Document Server (European Organization for Nuclear Research) · Cited by 6

Nuclear Physics Mid Term Plan at LNGS

Buompane, R., Cavanna, F., Curceanu, C., D’Onofrio, A., Leva, A. D., Formicola, A., Gialanella, L., Gustavino, C., Imbriani, G., Junker, M., et al. (2024) · The European Physical Journal Plus · doi:10.1140/epjp/s13360-023-04840-2 · Cited by 5

Carleman Estimates of Refined Stochastic Beam Equations and Applications

Yu, Y., & Zhang, J. (2022) · SIAM Journal on Control and Optimization · doi:10.1137/21m1463513 · Cited by 5

Untangling dissipative and Hamiltonian effects in bulk and boundary-driven systems

Renger, D. R. M., & Sharma, U. (2023) · Physical review. E · doi:10.1103/physreve.108.054123 · Cited by 5

Diffusion approximation for multi-scale McKean-Vlasov SDEs through different methods

Hong, W., Li, S., & Sun, X. (2024) · Journal of Differential Equations · doi:10.1016/j.jde.2024.09.012 · Cited by 5

Pseudo generators for under-resolved molecular dynamics

Bittracher, A., Hartmann, C., Junge, O., & Koltai, P. (2015) · The European Physical Journal Special Topics · doi:10.1140/epjst/e2015-02422-y · Cited by 6

Generalized conditional transform with respect to the Gaussian process on function space

Lee, I. Y., Chung, H. S., & Chang, S. J. (2015) · Integral Transforms and Special Functions · doi:10.1080/10652469.2015.1070149 · Cited by 5

Entropy Anomaly in Langevin–Kramers Dynamics with a Temperature Gradient, Matrix Drag, and Magnetic Field

Birrell, J. (2018) · Journal of Statistical Physics · doi:10.1007/s10955-018-2162-2 · Cited by 5

On Stochastic Differential Inclusions with Current Velocities

Gliklikh, Y. E., & Makarova, A. V. (2015) · Journal of Computational and Engineering Mathematics · doi:10.14529/jcem150303 · Cited by 5

An Application of Pontryagin’s Principle to Brownian Particle Engineered Equilibration

Muratore-Ginanneschi, P., & Schwieger, K. (2017) · Työväentutkimus Vuosikirja · Cited by 5

Contact statistics in populations of noninteracting random walkers in two dimensions

Rast, M. P. (2022) · Physical review. E · doi:10.1103/physreve.105.014103 · Cited by 5

Accelerated Diffusion-Based Sampling by the Non-Reversible Dynamics with Skew-Symmetric Matrices

Futami, F., Iwata, T., Ueda, N., & Sato, I. (2021) · Entropy · doi:10.3390/e23080993 · Cited by 5

Wiener Process

Malliaris, A. G. (1990) · Palgrave Macmillan UK eBooks · doi:10.1007/978-1-349-20865-4_43 · Cited by 5

Mobility Estimation for Langevin Dynamics Using Control Variates

Pavliotis, G. A., Stoltz, G., & Vaes, U. (2023) · Multiscale Modeling and Simulation · doi:10.1137/22m1504378 · Cited by 5

Stochastic quantization of an interacting classical particle system

Scarfone, A. M. (2007) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2007/03/p03012 · Cited by 4

Stochastic Leontieff-Type Equations with Multiplicative Effect in Spaces of Complex-Valued "Noises"

Shestakov, A. L., & Sagadeeva, M. A. (2014) · Bulletin of the South Ural State University Series Mathematical Modelling Programming and Computer Software · doi:10.14529/mmp140412 · Cited by 5

Strong invariance principle for singular diffusions

Heunis, A. J. (2003) · Stochastic Processes and their Applications · doi:10.1016/s0304-4149(02)00222-3 · Cited by 5

Bose-Einstein condensation: a transition to chaos result

Ugolini, S. (2012) · Communications on Stochastic Analysis · doi:10.31390/cosa.6.4.05 · Cited by 5

A lattice and random intermediate point sampling design for animal movement

Eisenhauer, E., & Hanks, E. M. (2020) · Environmetrics · doi:10.1002/env.2618 · Cited by 5

Reduction of non linear problems to Schrödinger or heat equations: Formation of kepler orbits, singular solutions for hydrodynamical equations

Albeverio, S. A., Blanchard, P., & Høegh-Krohn, R. J. (1985) · Lecture notes in mathematics · doi:10.1007/bfb0101545 · Cited by 5

Discrete quantum theory

Shale, D. (1982) · Foundations of Physics · doi:10.1007/bf00729805 · Cited by 5

A stochastic phase-field model determined from molecular dynamics

von Schwerin, E., & Szepessy, A. (2010) · ESAIM Mathematical Modelling and Numerical Analysis · doi:10.1051/m2an/2010022 · Cited by 5

Relativistic brownian motion

Caubet, J.-P. (1975) · Lecture notes in mathematics · doi:10.1007/bfb0068583 · Cited by 5

The correspondence limit of the atomic elliptic state

Durran, R., Neate, A., Truman, A., & Wang, F. (2008) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/84/30003 · Cited by 5

Probabilités et fluctuations quantiques

Fliess, M. (2007) · Comptes Rendus Mathématique · doi:10.1016/j.crma.2007.04.001 · Cited by 5

Risk, randomness, crashes and quants

Farhadi, A., & Vvedensky, D. D. (2003) · Contemporary Physics · doi:10.1080/0010751031000077396 · Cited by 5

Square integrable martingales orthogonal to every stochastic integral

Parthasarathy, K. R. (1978) · Stochastic Processes and their Applications · doi:10.1016/0304-4149(78)90034-0 · Cited by 5

Ornstein–Uhlenbeck process, Cauchy process, and Ornstein–Uhlenbeck–Cauchy process on a circle

Liu, C.-S. (2013) · Applied Mathematics Letters · doi:10.1016/j.aml.2013.04.009 · Cited by 5

The 2005 Neyman Lecture: Dynamic Indeterminism in Science

Brillinger, D. R. (2011) · Springer eBooks · doi:10.1007/978-1-4614-1344-8_25 · Cited by 5

Stochastic Leontieff type equations with non-constant coefficients

Gliklikh, Y. E., & Mashkov, E. Y. (2014) · Applicable Analysis · doi:10.1080/00036811.2014.940521 · Cited by 5

A solution of the nonlinear stochastic realization problem

Taylor, T. J. S., & Pavon, M. (1988) · Systems & Control Letters · doi:10.1016/0167-6911(88)90084-9 · Cited by 5

Thermal fluctuations and stability of a particle levitated by a repulsive Casimir force in a liquid

Inui, N., & Goto, K. (2013) · Physical Review E · doi:10.1103/physreve.88.052133 · Cited by 5

The Formulation of Quantum Mechanics

Davidson, M. (1998) · WORLD SCIENTIFIC eBooks · doi:10.1142/9789810248604_0003 · Cited by 5

Dynamic and plasmonic response exhibited by Au nanoparticles suspended in blood plasma and cerebrospinal fluids

Morales-Bonilla, S., Martines-Arano, H., Torres, D. T., et al. (2019) · Journal of Molecular Liquids · doi:10.1016/j.molliq.2019.02.073 · Cited by 5

Derivation of the Schrödinger equation based on a fluidic continuum model of vacuum and a sink model of particles

Wang, X. (2014) · Physics Essays · doi:10.4006/0836-1398-27.3.398 · Cited by 5

Ornstein–Uhlenbeck Path Integral and Its Application

Ezawa, H. (2000) · Acta Applicandae Mathematicae · doi:10.1023/a:1010780220954 · Cited by 5

Limit theorems for stochastic processes associated with a boson gas

van den Berg, M., & Lewis, J. T. (1988) · Lecture notes in mathematics · doi:10.1007/bfb0077913 · Cited by 5

Configurational Statistics of Macromolecules in Solution from Correlations of Liquid Molecules

Mezzasalma, S. A. (2006) · The Journal of Physical Chemistry B · doi:10.1021/jp063539d · Cited by 5

On the Kramers Very Low Damping Escape Rate for Point Particles and Classical Spins

Byrne, D. J., Coffey, W. T., Dowling, W. J., et al. (2014) · Advances in chemical physics · doi:10.1002/9781118949702.ch7 · Cited by 5

Stochastic spin-one massive field

Lim, S. (1984) · Physics Letters B · doi:10.1016/0370-2693(84)90306-x · Cited by 5

Scattering into cones and flux across surfaces in quantum mechanics: A pathwise probabilistic approach

Posilicano, A., & Ugolini, S. (2002) · Journal of Mathematical Physics · doi:10.1063/1.1504884 · Cited by 4

On nonlinear irreversible processes I

Ueyama, H. (1976) · Physica A Statistical Mechanics and its Applications · doi:10.1016/0378-4371(76)90008-x · Cited by 5

Stochastic interpretations of nonrelativistic quantum theory

Lavenda, B. H., & Santamato, E. (1984) · International Journal of Theoretical Physics · doi:10.1007/bf02214133 · Cited by 5

On geometric ideas which lie at the foundation of quantum theory

Shale, D. (1979) · Advances in Mathematics · doi:10.1016/0001-8708(79)90041-0 · Cited by 5

Backward representation for nonstationary Markov processes with finite state space

Masi, G. B. D., & Kitsul, P. I. (1994) · Systems & Control Letters · doi:10.1016/0167-6911(94)90088-4 · Cited by 5

Brownian Motion and Potential Theory

Taylor, M. E. (1996) · Applied mathematical sciences · doi:10.1007/978-1-4757-4187-2_5 · Cited by 5

Critical diffusions

NELSON, E. B. (1985) · Lecture notes in mathematics · doi:10.1007/bfb0075835 · Cited by 5

A second order equation for Schrödinger bridges with applications to the hot gas experiment and entropic transportation cost

Conforti, G. (2018) · Probability Theory and Related Fields · doi:10.1007/s00440-018-0856-7 · Cited by 51

Quantum mechanics as demanded by the special theory of relativity

Harding, C. (1977) · Foundations of Physics · doi:10.1007/bf00715242 · Cited by 4

Mathematical topics in compressible flows from single‐phase systems to two‐phase averaged systems

Bresch, D., Narbona-Reina, G., Burgisser, A., et al. (2024) · Studies in Applied Mathematics · doi:10.1111/sapm.12739 · Cited by 4

Quantum Theory of Irreversibility: Open Systems and Continuum Mechanics

Sewell, G. L. (2003) · Lecture notes in physics · doi:10.1007/3-540-44874-8_1 · Cited by 4

Fundamental formulas for modified generalized integral transforms

Chung, H. S. (2020) · Banach Journal of Mathematical Analysis · doi:10.1007/s43037-019-00048-8 · Cited by 4

Guest-protein incorporation into solvent channels of a protein host crystal (hostal)

Sprenger, J., Carey, J., Schulz, A., et al. (2021) · Acta Crystallographica Section D Structural Biology · doi:10.1107/s2059798321001078 · Cited by 4

Analytic continuation of stochastic mechanics

Kuipers, F. (2022) · Journal of Mathematical Physics · doi:10.1063/5.0073096 · Cited by 4

Stochastic Equations and Inclusions with Mean Derivatives and Some Applications

Gliklikh, Y. E., & Zheltikova, O. O. (2013) · Methodology And Computing In Applied Probability · doi:10.1007/s11009-013-9373-4 · Cited by 4

Magnetic-Field-Assisted Diffusion Motion of Magnetic Skyrmions

Qin, G., Zhang, R., Yang, C., et al. (2022) · ACS Nano · doi:10.1021/acsnano.2c03046 · Cited by 4

TouchNoise

Berndt, A., Al-Kassab, N., & Dachselt, R. (2015) · doi:10.1145/2814895.2814896 · Cited by 4

Langevin Equations in the Small-Mass Limit: Higher-Order Approximations

Birrell, J., & Wehr, J. (2020) · Annales Henri Poincaré · doi:10.1007/s00023-020-00910-8 · Cited by 4

A parameter estimator based on Smoluchowski–Kramers approximation

He, Z., Duan, J., & Cheng, X. (2018) · Applied Mathematics Letters · doi:10.1016/j.aml.2018.10.011 · Cited by 4

Image Solution of Stochastic Differential Equation of Diffusion Type Driven by Brownian Motion

Pandey, V. K., Agarwal, H., & Aggarwal, A. K. (2021) · Communications in computer and information science · doi:10.1007/978-981-16-1092-9_46 · Cited by 4

The Pyt'ev-Chulichkov Method for Constructing a Measurement in the Shestakov-Sviridyuk Model

Sagadeeva, M. A., Bychkov, Е. V., & Tsyplenkova, O. N. (2020) · Bulletin of the South Ural State University Series Mathematical Modelling Programming and Computer Software · doi:10.14529/mmp200407 · Cited by 4

THE SHOWALTER-SIDOROV AND CAUCHY PROBLEMS FOR THE LINEAR DZEKZER EQUATION WITH WENTZELL AND ROBIN BOUNDARY CONDITIONS IN A BOUNDED DOMAIN

Sviridyuk, G. A., GONCHAROV, N. S., & Загребина, С. А. (2022) · Bulletin of the South Ural State University series Mathematics Mechanics Physics · doi:10.14529/mmph220106 · Cited by 4

Complex Dirichlet Forms: Non Symmetric Diffusion Processes and Schrödinger Operators

Albeverio, S. A., & Ugolini, S. (2000) · Potential Analysis · doi:10.1023/a:1008610425255 · Cited by 4

Probability and quantum mechanics the conceptual foundations of stochastic mechanics

Guerra, F. (1984) · Lecture notes in mathematics · doi:10.1007/bfb0071718 · Cited by 4

Ornstein-Uhlenbeck Path Integral and Its Application

Ezawa, H. (2001) · Springer eBooks · doi:10.1007/978-94-010-0842-6_7 · Cited by 4

Stochastic variational principle and diffusion processes

Blanchard, P., & Zheng, W. (2008) · Springer eBooks · doi:10.1007/3540171665_58 · Cited by 4

Quantum mechanics as a stochastic process with aU(1) degree of freedom

Rosenstein, B. (1984) · International Journal of Theoretical Physics · doi:10.1007/bf02081000 · Cited by 4

Measurement and reduction of wavefunction in stochastic mechanics

Jibu, M., Misawa, T., & Yasue, K. (1990) · Physics Letters A · doi:10.1016/0375-9601(90)90248-m · Cited by 4

The underlying Brownian motion of nonrelativistic quantum mechanics

Santamato, E., & Lavenda, B. H. (1981) · Foundations of Physics · doi:10.1007/bf00726943 · Cited by 4

Stochastic and quantum space-time metrics and the weak-field limit

Namsrai, K. (1991) · International Journal of Theoretical Physics · doi:10.1007/bf00671983 · Cited by 5

The Green–Kubo formula for general Markov processes with a continuous time parameter

Yang, F., Chen, Y., & Liu, Y. (2010) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/43/24/245002 · Cited by 4

Quantum Macrostatistical Picture of Nonequilibrium Steady States

Sewell, G. L. (2004) · Letters in Mathematical Physics · doi:10.1007/s11005-004-4883-1 · Cited by 4

Quantum-like diffusion over discrete sets

Battaglia, D. A., & Rasetti, M. (2003) · Physics Letters A · doi:10.1016/s0375-9601(03)00679-0 · Cited by 4

THE EFFECT OF IONIC MIGRATION AND DIFFUSION ON THE ROUGHNESS DEVELOPMENT OF GROWING ELECTRODEPOSITS. THE USE OF FRACTALS TO COMPARE THEORY WITH EXPERIMENTAL RESULTS

Godorr, S., Young, B. D., & Bryson, A. W. (1992) · Chemical Engineering Communications · doi:10.1080/00986449208936073 · Cited by 4

A stochastic Hamilton-Jacobi theory in stochastic Hamiltonian mechanics for diffusion processes

Misawa, T. (1987) · Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B · doi:10.1007/bf02726581 · Cited by 4

Stochastic coupling and thermodynamic inequalities

Thomas, L. E. (1980) · Communications in Mathematical Physics · doi:10.1007/bf01269920 · Cited by 4

Schrödinger's interpolating dynamics and burgers' flows

Garbaczewski, P., Kondrat, G., & Olkiewicz, R. (1998) · Chaos Solitons & Fractals · doi:10.1016/s0960-0779(97)00046-5 · Cited by 4

Diffusion models for chemotaxis: a statistical analysis of noninteractive unicellular movement

Watkins, J. C., & Woessner, B. (1991) · Mathematical Biosciences · doi:10.1016/0025-5564(91)90065-q · Cited by 4

Lagrange lemma and the optimal control of diffusion. 1. Differentiable multipliers

Kosmol, P., & Pavon, M. (2005) · Proceedings of the IEEE Conference on Decision & Control, including the Symposium on Adaptive Processes · doi:10.1109/cdc.1992.371438 · Cited by 4

Fluctuations of bridges, reciprocal characteristics and concentration of measure

Conforti, G. (2018) · Annales de l Institut Henri Poincaré Probabilités et Statistiques · doi:10.1214/17-aihp844 · Cited by 4

Quantization in Financial Economics: An Information-Theoretic Approach

Hawkins, R. J., & Frieden, B. R. (2017) · Palgrave Macmillan UK eBooks · doi:10.1057/978-1-137-49276-0_2 · Cited by 5

Stability of the overdamped Langevin equation in double-well potential

Sandrić, N. (2018) · Journal of Mathematical Analysis and Applications · doi:10.1016/j.jmaa.2018.07.043 · Cited by 4

Entropy Flux in Stochastic and Chaotic Loewner Evolutions

Shibasaki, Y., & Saito, M. (2020) · Journal of the Physical Society of Japan · doi:10.7566/jpsj.89.113801 · Cited by 4

The Formulation of Quantum Mechanics

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Lévy Walk Dynamics in an External Constant Force Field in Non-Static Media

Zhou, T., Xu, P., & Deng, W. (2022) · Journal of Statistical Physics · doi:10.1007/s10955-022-02904-8 · Cited by 4

Energy of Markov chains

Syski, R. (1979) · Advances in Applied Probability · doi:10.2307/1426954 · Cited by 4

Quantum uncertainty relations and stochastic mechanics

Martino, S. D., & Siena, S. D. (1984) · Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B · doi:10.1007/bf02748969 · Cited by 4

Asymptotic Behaviour of Densities for Nelson Processes

Petroni, N. C. (1995) · Springer eBooks · doi:10.1007/978-1-4899-1391-3_4 · Cited by 4

Anderson’s Brownian motion and the Infinite Dimensional Ornstein-Uhlenbeck Process

Lindstrøm, T. (1995) · Springer eBooks · doi:10.1007/978-94-015-8451-7_16 · Cited by 4

Dynamical evolution in non-commutative discrete phase space and the derivation of classical kinetic equations

Dimakis, A., & Tzanakis, C. (2000) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/33/30/301 · Cited by 4

Quantum mechanical low energy scattering in terms of diffusion processes

Albeverio, S. A., Blanchard, P., Gesztesy, F., et al. (1985) · Lecture notes in mathematics · doi:10.1007/bfb0101546 · Cited by 4

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